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I love this subject, I liked it when I studied it too... When entropy decreased we called that an open system, otherwise it was closed. Like life on earth has a decreasing entropy. That's an open system. But when we take the sun and the energy that's coming from it the system will have an increasing entropy, now the system is closed...
In the specific simulation you showed at 4 minutes the particles actually attract each other which is why it springs back. So the particles are pulled to the center of mass, but one end is anchored causing all particles to migrate left.
I'm a physics student, and to my limited knowledge, the entropy of the dice did decrease. But the process still happened because of the release of potential energy when a die falls. The spontaneity may be determined by the change in the Gibbs free energy, which is given by dG = dQ - TdS (assuming isothermal and isobaric process). If dG < 0, the process is spontaneous. This is because the increase of entropy of the surrounding (-dQ/T) compensates for the decrease of entropy of the system (dS), thus abiding by the second law of thermodynamics. In this particular case presented in the video, since the system is not isolated (meaning, work and heat can trespass the boundary of the system), the decrease of entropy of the dice is compensated by the increase of entropy of surrounding caused by the release of heat that generated by the falling of the dice. I genuinely enjoy every video of yours! Thanks for uploading such an amazing video :)
This makes intuitive sense. The demostrations in the video are wonderful to teach how crystals form: the particles slot in the position with the lowest bonding potential energy, in the same way as the dice and nails slot in the position with the lowest gravitational potential energy. Would you agree? (PS honest question: I'm a high school teacher who has to teach chemistry with a degree in botany 😅)
My understanding is that increases in entropy are increases in homogeneity. In other words, one subregion of a high-entropy region should be difficult or impossible to tell apart from an adjacent subregion with the same level of entropy. To me, that sounds like a crystal lattice. The term "order" was, IMO, originally slightly misused when the terminology for talking about entropy was getting established, since some of the physical effects of increased entropy are at odds with our natural language use of the term "order" (and its inverse, disorder) to refer to things like how tidy your room is, or how regular a printed pattern is.
@@Mikee512 the third principle of thermodynamics can be stated as "a perfect crystal at 0K has 0 entropy", which to me seems at odds with this interpretation. A perfect crystal would be perfectly homogeneous, with each region indistinguishable from any other, corresponding to a single microstate. Am I wrong? 🤔
Another thing to consider The dice and nails also reached a state where the gravitational potential energy of the system was minimized, the disordered arrangement took up more volume meaning there were lower states the dice could be in if organized. The gravitational potential energy was thus, dissipated as sound and heat. This is equivalent to the nature of living systems. They exist in what we would call a more ordered state, but their capacity for converting useful forms of energy to waste heat more than offsets any apparent decrease in any other aspect of entropy they cause.
Seems work was done on the system with the twisting torque input or shaking the nail box. That kinetic energy converted to waste sound/heat means entropy increases. Gravity is another static input to the system.
Gotta disagree with the reasoning that there is more entropy in the ordered dice because they are more compact and "have more room to move around." They only have more room compared to the height of the disordered state. The dice are not actually concerned about the height of the disordered state, so I would argue that they are in fact at lower entropy since the room they care about (to the sides and below them due to gravity), is less, and there are fewer opportunities for the dice to move around.
I think this is true if you only look at the dice. But we are looking at and comparing the system in a packed state vs a random orientation state. When looking at the system as a whole we must keep the volumes the same.
Yeah. Entropie relates to the number of microscopic states that have the same macroscopic properties. The ordered dice have lower entropy since there are fewer such ordered states than unordered states (roughly, you can orient an ordered die in 24 ways, an unordered one in many more ways). The fact that the system spontaneously becomes ordered does not mean that that order has higher entropy.
This is incorrect. When the dice are disordered, many of them are effectively jammed and can't move at all. On the other hand, when the dice are ordered, each dice is free to move a little bit. They don't have much room, but remember that entropy is related to the number of possible microstates. It increases with the factorial of the number of dice when they can all move. Entropy-driven crystallization is an entire field of study. It's really counter-intuitive, but the explanation in this video is correct.
@@cwpeterson87 Dice don't have to move for entropy calculations; moreover, if they are well packed they would also not move. That is a red herring imho. I could for instance swap dice (even if they are blocked, I can still imagine two states that differ by a swap); thát gives multiple microstates with the same macrostate. Similar other processes like that. Most compelling to me is that this is completely analogous to crystallisation, and a crystal has lower entropy than - say - the corresponding gas. There are lots of other effects here. Like, the dice fall down, thus decrease in gravitational energy, which energy is dissipated such that the dice warm up. And thát heating still increases entropy in compensation. (They release heat, just like crystallisation does btw.) The argument in the video that the packed dice have air above them to move to is not correct either in my view: it requires energy for dice to move up there against gravity, so that is no longer the same macrostate; it has different total energy. (And on top of that, the jumbled dice leave exactly the same room for air among each other.)
I was really just thinking about what implications this phenomena has on living organism behavior, not just these inanimate objects that are being observed for the video
Excellent video, but I think you have it wrong with regard to the dice and nails. They settle when jostled into the lowest energy state - that being the lowest overall point in the gravitational field they are in. Do the same thing in a location without gravity and you'll get different results. I agree with the rubber band example however. Note that stretching a rubber band heats up the rubber, and it cools again when it contracts. This is consistent with entropy. The nails and dice would also heat up (or increase in average speed) if you jostled them in zero gravity just like the rubber by the amount of energy expended to jostle/stretch. Entropy is simply a measure of how likely a configuration is. Sure, it's possible that rubber band could stretch itself just sitting on my desk, but with 100's of billions of molecules in it all needing to do essentially the same thing at the same time over a long period of time (contextually speaking) a mathematician would call it a statistical impossibility.
I'm not sure about the rubber band one personnally, and if their is a contribution the force produced would be almost nothing compared to the intra and inter molecular force involved in an elastic.
@knurlgnar24 Agreed, Action Lab reversed the scale conventionally used to measure entropy. The disordered box of nails should be said to have relatively higher entropy than the more ordered box. I stopped watching after that botched intro.
I think if whoever the first person to use the word "disordered" to dscribe entropy had instead used "homogenous" or something I think we'd be like 50 years ahead with our understanding of physics and information theory
Doesn't work either : case in point oil does not mix with water, and homogeneous emulsions separate into distinct layers. The first use of entropy came from the observation that heat transferts spontaneously goes from hot stuff to cold stuff, and that this puts a hard limit on how efficient a thermal engine can be. The modern understanding of entropy is that it is a measure of the number of microscopic states a system can be in based on the values of observables that can be measured at our scale. The channel alphaphoenix made a really good video recently if you want a more in depth explanation.
"homogenous" is closer but not quite right. I think "likelihood" is a better description but still not perfect. If you allow a system to evolve undisturbed for an arbitrarily long amount of time, taking observations at random times, higher entropy states are more likely to be observed over time.
To me the best description of entropy is it’s the act of something reaching its most stable state. Like with these dice being organized like that the dice is more stable than when they are disorganized. Rust is chemically more stable than iron.
2:35 sounds fishy... please check: 1. microstates in the Bolzmann formula have the same energy. Here, if any dice goes to the free space above, the system will have its energy increased by the work against gravity. This breaks the condition of the microcanonical ensemble 2. Microstates are equally possible, however we don't see dices jump into the free space by their own will, therefore the shown state has much larger probability to be in and this breaks the condition of the microcanonical ensemble
I agree with your description, but bear in mind that this system wouldn't be described by a microcanonical ensemble, because it is not isolated. In fact, Boltzmann entropy would not be the correct expression for entropy in this case I reckon. This looks more like a (N, g, T) ensemble, where available states are definitely not iso-energetic. Further thought is necessary on my part
@@andreacosta7712I guess you've meant canonical NVT ensemble. I agree with you, it should be more suitable in this case. However, I played along with the author, who decided not to introduce Gibb's formula. However even if the energy distribution of microstates was considered, my point (2) would still hold. I actually try to lead to an idea that the author has some sense in his words only if he never stops shaking the jar and even in this case it could be hard to say smth specific about energy distribution of states and the resulting entropy
Definitely, any kind of thermodynamical reasoning only holds if the shaking is ongoing, aka constant temperature. What I meant was indeed NgT. Volume is not constant, but gravity is. In a way, a constant-force ensemble is equivalent to a constant-pressure one, as in NpT, which is described by Gibbs free energy. My general point is that in this demo, the interplay of energy and entropy is what actually explains the phenomenon, so reasoning in a microcanonical framework does not give you the full picture, because entropy is constant in it. But yes, point 2) still holds.
@@JackAtlassBasically, these are bad examples using the wrong math, failing to state the things he wants to state even though what he's saying is true. He's wrong in every step of explaining why it's true.
This is a wrong explanation. The spontaneous orderly arrangement in the example is due to the effect of gravity. Dice can lower their overall center of gravity when arranged neatly, and the same is true for nails. If gravity is removed, such as by astronauts conducting experiments in the space station, you will see that neither the dice nor the nails will spontaneously organize neatly.
@@andymouse Maybe It approximates the dark matter flowing over and through us. Galaxies start out as ring galaxies and "acquire" arms and bars and get warped along their rotational equator and things due to perturbations from other stimulus. An in space simulation would be all the dice in the cylinder in a random meander. Similar to a space containing a gas. It would take longer than it takes for tar to drip to get the data.
But if you remove the gravity of Earth or any other massive object the dice themselves would still gravitationally attract each other and they would form a clump with mostly face to face contact, very similar to the way they are arranging in the bottom of the tube.
'Amount of free volume per dice increases'. I thought that the amount of free volume is the same before and after aligning dice in a finite system, it is just that the same 'old' free volume is now concentrated in 'new' free volume in space continuously, above the dice, not scattered between dice.
yep - If we follow this guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same. (If we are allowed to reduce the volume in the ordered dice system, Then it has lower entropy.)
Ehy, I haven't checked the entropy calculations for the dice problem, but I have the feeling that the problem can be formalized in a way to define a free energy (akin to Gibbs free energy for chemical systems at conatan p and Helmoltz free energy at constant V) for the system as a combination of entropic effects and energetic effects. The energy in this case is given by the gravitational field and the constraints of the jar. If you had the same jar (with a lid, to make things simpler) in space, the average equilibrium state would be the one with the disordered dice scattered all over the place. I think that the only reason why you reach the ordered configuration with your shaking process is because that configuration corresponds to the local minimum of free energy for the system in the gravitational field. The shaking is just a way to go from local minimum to local minimum until you have reached the global minimum. The fact that the equilibrium of systems subject to forces is not the maximum of entropy is a well known fact in chemical thermodynamics. In fact, almost always, maximizing the entropy doesn't give you the chemical equilibrium of a system. Otherwise you could not explain things like the formation fo crystals or even molecules at all. The second principle of TD tells you that entropy is a thermodynamic potential only strictly for isolated systems: for all other systems, you need to find a suitable TD potential to minimize or maximize given the constraints of the system. The only thing that TD (specifically, non equilibrium TD) tells you about entropy is that any irreversible process comes with a positive entropy PRODUCTION (not entropy): but for any non-isolated system, you can always let entropy in and out of the system by suitable fluxes of heat or mass. Finally, I am sure you are familiar with the fact that since Boltzmann's pioneering work on the statistical interpretation of entropy, there have been several different definitions of "entropy" related to microstates of the system, more or less coherent with each other and the classic definition of entropy proposed by Clausius. Even without entering the rat's nest of which statistical definition of entropy you are referring to, I would honestly be surprised if you cannot find a coherent formalism in terms of free energy to describe the entropy of the dice so that it indeed decreases as it approaches final metastable configuration, thus attributing the driving force to an energetic factor.
To my understanding entropy describes particles "desire" to reduce their energy to reach the most stable state. The dice prefer the tightly packed state because here they have the lowest amount of potential energy. Also it takes a lot more energy to break that state apart, because the previous unorganized state could be broken apart by the tapping / rotating, the new state however is hardly affected by it.
Indeed. When you have packed particles, if you free them on a bigger room, they redistribute to reduce their energy. On the dice scenario, this happens also for reduce their energy.
Nice video, but Entropy in the original statistical mechanics sense of S=log(Omega) is good assumption ONLY in an energy conserving equilibrium system, what is generally called a microcanonical condition. In the case of macroscopic spheres (or dice) you have a dissipative system in which a lot of energy is dissipated into heat during collision and this is why you have to provide energy by vibration. This is a steady state and not an equilibrium one and entropy technically is not defined. Clearly you can use the dice example for pedagogical reason, but with a bit of care. You said: "any system wants to maximize entropy" this is not true. Let me give an exanple. If you wold have a mixture of two macroscopic spheres in a shaker they will have a strong tendency to demix with the big spheres going on the top (brazilian nuts effect). In a equilibrium system this will be nuch more unlikely (especially if rhe sizs ratio of the two spheres is not too large) because mixing increase the number of condigurations and consequently entropy.
The trick here is not to compare the original disordered dice configuration to the final ordered one, but rather to imagine the distribution of dice orientations while the container is being shaken. At equilibrium, most of the dice align and the ones near the top are constantly and rapidly bouncing around. If the container is not being shaken, the entropy of both configurations near zero because the dice have almost no probability of changing state. And analyzing the situation becomes harder because the disordered configuration will have a higher energy level due to potential energy than the ordered configuration
This is true but a more practical role would involve calculating the partition function. We need to incorporate positional and configurational entropy due to the limited volume. This would be more a more detailed approach and would incorporate both positional and potential energy considerations.
If we replaced the dice with smaller particles like those Einstein first observed brownian motion in, it seems clear the unpacked disorganized dice are much higher entropy. Random disturbances are much more likely to lead to an unpacked vs packed state. For every 1 packed permutation, an enormous number of translated identical ones. Am I missing something?
3:33 This is semantically untrue. The reason the rubber band returns to an unstretched state is because of electrostatic attraction and repulsion between the molecules within the rubber, which respectively resist stretching and compression, and thus effectively function as an elastic force. You can explain this as a mechanism that acts to increase entropy, but this does not change the fact that the force is elastic in nature.
The ordered jar has less entropy, with the dice compacted there is less positions they can actually occupy while still looking the same in buik; but the total entropy of the Universe increased with the heat of the friction and collisions though. Just like life, we may seem to violate the laws of thermodynamics with all our growing and reproducing, but it's actually the opposite, we spread heat more easily than still rocks.
The story of the dice themselves decreased, but the entropy inside the jar as a whole increased as a result by compacting the volume. Honestly though, he is using semantics.
That's incorrect, energy neither increases or decrease, the universe is moving towards the most statistically likely configuration which is the true definition of entropy. *The 3 levels of entropy from less correct to more correct* 1: A system moving in the direction of a more disorderly state 2: A system moving towards a state of equilibrium 3: Energy and matter displaying the most statistically likely configurations *Creating the arrow of time by moving towards that given configuration that can be more or less statistically likely but the ones which are the most likely are considered entropy
@@notaffiliatedwith7363It's not about geometry and order, it's about the most likely configuration in a given system with it's laws of physics at work
@@markmuller7962 Yep, "order" and "disorder" are subjective, so they do not always match with the entropy. A good example is oil and water separating over time when with most other liquids we see the opposite.
@@jacobblaustein7779If the jar entropy has been increased, it's due to the heating while wildly shaking. The jar is not a closed system. Explanation is not valid, or not complete, while heat and sound noise are not considered, as well as random shaking.
What was said in the beginning of the video, that the 'ordered' systems (dice or spheres) have more entropy than the disordered ones is not correct (if we look at the isolated entropy of the packing of dices and spheres). You might consider correcting this. These systems do not reach a state of maximum entropy, but the minimum of an energy potential (like the Gibbs potential in thermodynamics). For the dices and the spheres this potential contains a gravitational energy term, which is the +m*g*h, where m is the total mass of the dices or spheres, g the gravitational constant and h the height of the center of mass of all the objects in question. The second term is an entropic one -c*S (c is some constant depending on the thermal energy or the shaking intensity in this case). The system now tends to adopt a configuration of minimum m*g*h-c*S. The close packing reduces h and this term dominates and therefore the dices or spheres adopt a packing where h is smallest possible even if S is not at its maximum. Here minimal h and maximum S can not be reached simultaneously. To understand this consider there is no gravity (i.e. g=0) then only the entropic term -c*S is left in the potential and the system will adopt the state of maximum entropy (i.e. all dices and sphere floating randomly in the cylinder) at the mildest shaking (i.e. c is not zero). The second case is strong continued shaking. In this case c will be very large and m*g*h will become negligible (basically g can be assumed to be 0). Then again the dices and spheres will ‘float’ randomly in the cylinder due to the shaking.
If he said 'maximum entropy' then he's wrong on that as you say. He's also mixed up on another count i'd say: If we follow the guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same. (If we are allowed to reduce the volume in the ordered dice system, Then it has lower entropy.)
Reminds me of how the initial state of the early universe would have appeared about as random/disordered as possible yet gravitationally speaking was very low entropy.
The initial state of the universe is extremely ordered. All matter existing in the same point. There is only one configuration for that to be the case.
@@JamesDevlin-d4z It wasn't a single point. The universe before the big bang was still infinitely large, it was just much, much more tightly packed. At least, according to the widely accepted theories.
I'm joining team "I don't agree". Because the dice in the ordered state have fewer opportunities to change position. If you keep doing that start stop they no longer move. Where in the disordered state they do move. Meaning the disordered state has more opportunities for the dice to move and therefor a higher level of entropy.
One way to clarify what he's talking about is if you understand entropy as hidden information rather than disorder (the latter of which I despise as an explanation of entropy). In this sense, free space has no information content, amd thus no hidden information. By lowering the average free space in the local vicinity of the dice, we are hiding more information, because now any given die could have any 6 other die (or 5, if it's against a wall) directly pressing up against it. This is the massive increase in translational entropy that he's referring to.
This is not entirely correct and in fact could be incorrect. It’s not black and white. We have to keep this simple and not try to manipulate individual concepts but instead focus on the combined perspective. Configurational entropy and positional entropy both need to be considered and calculated. If the extent of free volume significantly affects the number of Microstates that are accessible, then it’s possible the organized dice may have more entropy due to positional freedom. If the volume is more constrained, randomly orientated dice will have more entropy. We can not make the claim that one has more than the other without proper measurement.
If we follow this guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same. (If we are allowws to reduce the volume in the ordered dice system, Then it has lower entropy.)
*The 3 levels of entropy from less correct to more correct* 1: A system moving in the direction of a more disorderly state 2: A system moving towards a state of equilibrium 3: Energy and matter displaying the most statistically likely configurations *Creating the arrow of time by moving towards that given configuration that can be more or less statistically likely but the ones which are the most likely are considered entropy
(3) need a tweak: the whole point is that all microscopic configurations are equally statistically likely (at the same energy), but there are just so many more with the "right" macroscopic variables that it always looks right. e.g., the configuration of N2 and O2 molecules in the room (all your rooms) right now has the same likelyhood as the one with all O2 on the left side and all N2 on the right side, but there is only one state that looks like the latter, and more than Avagadro's number to the sixth factorial that look like the former, and (N_A^6)! >>>>>>>>>>>>>>> 1.
The "arrow of time" is not necessarily a more correct part of your difinition. An interesting idea, but not demonstrable. Sean Carroll (the physicist who proposed this) is a *theoretical* physicist and his idea arguably enters into an unprovable area.
@@PsymonHawkeye Actually the arrow of time is a side addition to the third concept just to make it clearer. And btw it's not a matter of hypothesis, the main role of entropy in the arrow of time is a theoretical physics *fact* aka scientific theory which doesn't have anything to do with the English popular use of "theory". It's a scientific theory, learn how science works
@@markmuller7962 agreed. Idk, that was my favorite part of statistical mechanics. I use it to disused lottery players: Me: “ you should pick 1,2,3,4,5,6” Them: “why? That will never come up!” Me: “exactly.”
I always understood entropy as the drive towards a stable state where no work is done, e.g. when all heat is evenly distributed in the universe, there is no transfer of energy (because heat doesn't pass from cooler to hotter (thank-you to Flanders and Swan for their song about the laws of thermodynamics) and everything is equally hot. The dice stop moving once they are aligned because the are then at their most stable configuration. In an earthquake, things fall down because being on the floor is their most stable state.
Hey! I like your video, but I have to ask for clarity. You treated the bowl of dice as a closed system while exerting outside forces. I believe you when you say the total entropy of the final system (inside the bowl only) increased, and the entropy of the drill also increased. Why was the outside force ignored? In another system where outside forces are ignored you may have decreases in entropy. But missing the outside force leaves the question open, does the entropy decrease in the bowl balanced by the entropy increase in the drill? Of course you explained that when looking at possible states it is favorable to pack. Further, thanks for the video, we fail to remember that "ordered" is a human imposed concept, if we define it as the low entropy states, then the bowl of none packed dice is more ordered than the packed one. But our brains like to call the packed state as more ordered.
As an aside, regarding "ordered" being a human imposed concept, I tend to think of "order" vs. disorder being recognizable patterns vs. a lack of recognizable patterns. Of course taking macro and micro into account, there are patterns that we don't always immediately recognize as such. You can quickly get into "does a tree falling in the woods make a sound if there's no one there to hear it" territory (we know the answer to that of course). Referring to whether patterns/order requires observation to be considered patterns/order vs. random chaos. The science of the impact or lack thereof of observastion of phenomena in the universe continues to be intriguing topic.
I'm confused. The number of configurations of the ordered state is smaller because the number of possible configurations is limited to permutations of the dice with their neighbors. As opposed to the disordered system, where they can permute with their neighbors as well as form various other random disordered configurations largely indistinguishable from the particular state this system happened to be in before you did work to it. What am I missing? Is this a feature of being in a central force field? The fact that the potential energy of the system as a whole is higher if it has dice are at a higher level, and the "relaxation" of this system to a lower energy state is the key? This is how I see it differs from the box example where the lower energy state is the even mixing. We needed to do work to put them in the corner, since their tendency is to NOT be in the corner. This is reversed here due to gravity even though you had to do work to the system by shaking it to order them.
My understanding is that the jar with the dice packs in an ordered way because that decreases the total gravitational potential energy of the dice, which makes that state more likely. If jar were in a state of weightlessness, the disorganised state would be more likely.
The second law of thermodynamics applies to closed systems, not all systems in the universe, nor all theoretically possible universes... But an interesting video that will be fun to think about.
yep - If we follow this guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same. (If we are allowed to reduce the volume in the ordered dice system, Then it has lower entropy.)
My thermodynamics professor had something he repeated constantly, "now we just count the states." Right, "just". The text (which he wrote and distributed free) had an explanation of how we knew all the states had been counted. Entropy was simple, the more states possible the higher the entropy and the more probable that the system would be in one of those states. Amazingly most of the laws of gases, liquids and even solids could be reduced from this "simple" counting of states. I'm not going to attempt counting the states of dice in random vs. ordered configurations but I'm pretty sure that from this perspective there are more states of randomly ordered dice. My lesson I learned is that the properties which apply to atomic level particles are not necessarily those that apply to macro sized objects.
@@JK_Vermont Not the issue. The video was claiming that volume was created. Not that usable volume was created or more useful volume was created. Details matter. "It's physics for Godsakes".
I saw it differently. The random dice in the glass has a higher potential energy state than the organized stacked state hence the jiggling tends to organize the dice.
@@nonabroladze8203 no it's not mess or disorder. they are just the more probable outcomes. it just mesures the number of arrangements particles can have(it have more to do with the distribution of energy rather than particles) . a cube of ice have almost one arrangement of atoms while vapor can have an astronomical amount of arrangements. vapor got more entropy than a cube of ice it's not about disorder. disorder just tend to corelate with it in most cases.
@@nonabroladze8203 as the guy showed in the video there are more ways to arrange the dice in an "ordered" maner than there are to arrange it in a disordered manner even if the entropy is high the cube arrangement will get more ordered with time.
I prefer to think of entropy as pointing in the direction of the arrow of time - jiggling and jostling over time will tend to produce the most common configurations. This only holds if all configurations are equally available and aren't sticky. Natural filters in life put a non-random bias against this jostling, from your example here to the gravity wells of stars and the motion of beaches, or Life's Ratchet in the cellular machinery. If once a random state occurs that locks in a position (like your orderly dice that can no longer move) then they will tend to order up even if order up states are less common, because they stick. No matter how slow the decay is or how uncommon the state of a random decay is, Schrodinger's cat will die when it happens and will stay dead (cat will randomly die but not randomly resurrect), so over long time you are much more likely to find a dead cat than a live one. Entropy was meant to describe states that are fully free to interact in the system, not natural filters. It doesn't break physics, it just doesn't fit that model. If you think of entropy not as of particle concentration or arrangement, but as the most likely outcomes over long times scale including non-random natural filters, then a compact star or beautifully orderly beach sand are actually low entropy as the dead end of the jostling options. This kind of one-way-ness also applies in other realms like gambling - where no matter how much you win you still can still risk all and lose all, but once you are broke you cannot un-lose. The house always wins even if you have slightly favorable odds, because even a less common disaster cannot be recovered while all cumulative success is just one bad roll from being wiped away.
Entropy? :D This is more about a constant field of gravity acting on the contents locking them in place, and the constant work input by agitation that allows each die/bead to move out of its current local minima and fall into its new place. Once slotted into positions, gravity and force from their neighbors restrict them from moving out of place. This effectively locks them in place. It just so happens that the most 'restrictive' spaces are also the most space-efficient structures (highest packing efficiency), and crystalline structures are quite space-efficient. Hence spheres forming a face-centered cubic instead of body-centered cubic or other patterns. Given the magnitude of forces at play, they drown out any entropy changes you see in the system. Try doing this test without agitation and gravity messing with the system. Try suspending them in solution of similar density. If you let the solution evaporate or drain slowly, it might shed a decent light on crystal formation too. (drain too fast and they will look more disordered, and 'crumbly' too) :D
Cool video! I have seen many confusing explanations of entropy, but on of the better ones is "Entropy states 'that which is most probable will probably happen.'" In a random system, the probabilities reflect that in disorder. If the rules of the system are ordered, the result will generally be ordered. In application it's a little more complicated than that, but in general essence it seems to be right. So I guess the entropic force is the tendency of the system to align to its underlying probabilities.
1:45 Well Said Remember Folks, AI will give you the Popular Answer, not Necessarily the Correct Answer. [Usually Popular = Correct AND you also want to Double Check some other way]
As others have already pointed out, gravity is also driving this process. When the blocks align with each other the overall center of mass is lower, so it's a lower energy state. It would be nice to test this in a zero G environment, but since those are hard to come by, I'll offer an alternative. If you can fabricate blocks of neutral buoyancy, the experiment could be repeated underwater. That would eliminate any effect of gravitational potential energy. It would be interesting to see the results.
"When enough chaotic and random events happens. Eventually, it leads to very predictable events." Thats quite philosophical. So after enough observations, everything will be understood.
Yet the definition of chaotic and random preclude the possibility of predicting. So are the events truly chaotic or random? If they are predictable then they can't be.
@@PhokenKuulthis is incorrect. There is nothing in the definitions of chaotic or random that preclude prediction. Dice rolls are random but I can accurately predict that each number will appear 1/6th of the time in a large number of rolls.
There are a couple things that don't make sense to me about this. And these aren't rhetorical questions, I absolutely believe your account of how it works since you know much more about it than I do. These are points of genuine and self-acknowledged confusion. 1) If entropy depends on number of possible configurations, shouldn't the dice still have higher entropy when more disordered? You say they have higher entropy when tightly packed because there's more free volume above them, but it seems to me the number of possible configurations of the dice is higher the more volume the dice _do_ occupy, not the more volume they _don't_ occupy. I realize the dice are actually separate objects, but if we think of the volume they occupy as this connected, amorphous cloud, then shouldn't there be more possible places we could find any given die in the larger _that cloud_ is, _not_ the larger the _air above it_ is? I guess what I'm getting at is, if we consider only the configurations where the dice are tightly packed, it seems to me the probability of finding any dice in the unoccupied volume above the dice, that volume you described as "free," is by definition _zero._ 2) Also, generally, how valid is it, really, to discuss entropy as a number of _possible_ configurations of a system which has a _known fixed_ configuration if closely observed? If die A _is_ at position P, and die B _is_ at position Q, then the probability of finding die A at position Q or die B at position P is zero. I know I just got through saying we can think of the occupied volume of the dice as this connected, amorphous cloud, but can we really? Isn't that occupied volume actually a precise crystal structure in the exact shape of a whole bunch of cubes, with pockets between them excluded from the manifold? By that logic, it seems to me that _everything_ has zero entropy at all times. I realize this notion of exact knowability doesn't hold at a quantum scale, where the uncertainty principles take effect, but we aren't _at_ that scale.
This really changed my understand of entropy and appreciate the perspective that life is an emergent property of a system that has evolved to increase entropy while efficiently dissipating energy. The variety of life on Earth shows that a relatively small number of different chemical elements can assume quite a variety of arrangements. Carbon is entropy's strongest proponent in that realm.
Action Lab reversed the scale conventionally used to measure entropy. The disordered box of nails should be said to have relatively higher entropy than the more ordered box.
he's wrong - If we follow this guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same. (If we are allowed to reduce the volume in the ordered dice system, Then it has lower entropy.)
I'm not an expert on entropy, but the easier explanation in my mind is that the aligned dice simply have more possible states available. Consider 100 dice stacked in the bottom of the container - each cube can be swapped for any other so you have a total of 100! possible states. Now imagine that 20 of them are sitting on the edge - each of the cubes lying flat can be swapped with each other flat cube (80! possible states), and each on-edge cube can be swapped with each other on-edge cube (20! possible states). So the mixed orientation configuration has 80! x 20! possible states which is SIGNIFICANTLY fewer states and therefore lower entropy. Adding additional orientations here lowers the entropy. (Yes, this is a simplification of the situation) I'm not yet totally convinced that the "free volume" concept is very helpful in understanding the increase in entropy with the dice here even though the difference in volume will certainly play a role in the number of states. Although it's pretty surprising, I wouldn't say there is anything "mysterious" about this "force". Where there are MANY more possible ways for a system to do something, the system will tend to eventually do that thing. At least, that's how I like to think about it.
I watch tour channel mainly for how you make science topics fun and engaging with clever and novel experiments, but then every so often you deliver powerful insights expressed really intuitively and clearly. Thank you. Excellent work.
When you jostle the dice, their gravitational potential energy is being dissipated as sound and heat, so they tend towards a "ground state" where their potential energy is minimized (by being packed as low as possible). The entropy of the dice does indeed decrease because there is only one "ground state" (up to rotation of each layer). It's possible for the dice's entropy to decrease because they are not a closed system - you are not counting the microscopic degrees of freedom where the sound and heat end up as part of the system, and if you did, total entropy would increase. Another way of looking at it is if there were no energy dissipation into those microscopic degrees of freedom, then the dice collisions would be perfectly elastic and they would keep bouncing around instead of settling.
I've quite recently finished writing my PhD thesis on entropic phase transitions in some specific systems. I have a whole section of a chapter devoted to "trading" one type of entropy for another type for a net entropic gain. I find this phenomenon very fascinating and almost each one of my scientific papers has a short, "intuitive" discussion how it is applied to the case on hand.
Since when does ChatGPT "represent most people"? STEM bros really crumble at the thought of social research, huh? You could've easily made a poll of your audience or cited popular definitions of entropy in recognized dictionaries but you chose the laziest way possible, somehow equating an LLM with "most people" as if it's a fact.
While the entropic force is a major factor in a rubber band's retraction, it's not the sole force at play. There are also: Enthalpic Forces: These arise from changes in the internal energy of the rubber band when stretched. Stretching stores energy in the polymer bonds, and releasing the band allows this energy to dissipate. Cross-linking: The polymer chains in rubber are often cross-linked, creating a network that resists deformation. This contributes to the overall restoring force. The Dominant Force: In most everyday situations, the entropic force is the dominant factor in a rubber band's behavior. This is why heating a rubber band (increasing entropy) causes it to contract, and cooling it (decreasing entropy) makes it stretchier. Important Note: The balance between entropic and enthalpic forces can change under extreme conditions (e.g., very high or low temperatures) or with different types of rubber. In summary: The entropic force is a significant factor in a rubber band's tendency to return to its relaxed state, but it's not the only force involved. Enthalpic forces and cross-linking also play a role, although their contribution is usually smaller in typical scenarios.
This is why science is so great. Its about studying whats actually going on regardless of preconceived ideas or beliefs. Properties of the Universe can get confusing (especially when there are multiple things going on and many variables). Science is studying each one, recording data, repeating, recording, etc. Humans love to see one event and assume they know everything from it...we know thats not the best way yet here we are in 2024 with 10s of millions who would rather believe what they want to more than what is real.
You have to be careful when talking about the entropy of one specific system with respect to another. Entropy can only be defined for an ensemble of systems that satisfy certain conditions. In the case of the cubes that are "axis-aligned" rather than with random orientations, does your ensemble include states where the cubes are floating in the extra air space you describe -- or does your ensemble only include microstates that are stable under gravity? If you only consider microstates that are stable under gravity, the extra volume gained will not be occupied by stable states. Hence, the "axis-aligned" system would seem to me to have less entropy, as our intuition would tell us. Furthermore, if we are to use the fact that all microstates are equally likely, it would make sense to limit our ensembles to "stationary states" that have long lifetime -- not states where die are momentarily in the air occupying that extra volume. If someone has a different interpretation or thinks I'm wrong in some way please let me know!
Once the universe reaches full entropy, if ever, that will be perfect order. Or as close as you can get to it. How people come to the conclusion that entropy is chaos is beyond me
I think the way that communicates best how I understood entropy is "The inverse deviation from an object's state at the end of time," meaning, the more entropy increases, the more closely an object will reflect the state it would be in as time approaches infinity, and that entropy is used as a way to gauge how far away an object is in an initial state from the state it will reach at the end of time
4:07 you say there's no forces acting on the particles making them coil together but actually in the simulator you used the electromagnetic force is simulated, which is what's pulling them together
Finally someone who gets it and can actually explain it in a good way.. Damn, not even my university profs got the concept of entropy! The whole "you can't unmix the marbles!" and other demonstrations of randomness to explain entropy completely ruined the idea in the public mind. We need more of these videos!
I got inspired to ask Gemini (my old friend) and it gave a similar answer to Chat GPT, so I fed it the transcript for this video, and Gemini agreed, so we concocted a question for Claude 3.5 together: If I have a box filled with randomly oriented playing cards and I shake it until all the cards are perfectly stacked by suit (hearts, diamonds, etc.), entropy has increased according to the second law of thermodynamics, even though the system appears more ordered. Can you explain why this happens, considering the concept of microstates and how they relate to entropy in this scenario? ANSWER: This is an excellent question that touches on some key concepts in thermodynamics and statistical mechanics. Let's break this down step-by-step to understand why entropy increases in this scenario, despite the apparent increase in order. Entropy and microstates: Entropy is a measure of the number of possible microscopic configurations (microstates) that a system can have. The more microstates available to a system, the higher its entropy. This is expressed mathematically by Boltzmann's equation: S = k * ln(W), where S is entropy, k is Boltzmann's constant, and W is the number of microstates. The initial state: When the cards are randomly oriented in the box, there are many ways to arrange them. Each unique arrangement is a microstate. The number of microstates for this "disordered" state is extremely high. The final state: When the cards are perfectly stacked by suit, it might appear more ordered macroscopically. However, we need to consider the entire system, including the surrounding air molecules and the box itself. Energy transfer: Shaking the box inputs energy into the system. This energy is transferred to the cards, the box, and the surrounding air molecules. The air molecules gain kinetic energy and move faster. Microstates of the entire system: While the cards become more ordered, the air molecules become more disordered. The number of possible arrangements (microstates) for these energetic air molecules is vastly larger than the number of microstates for the slower-moving air molecules in the initial state. Total entropy change: The decrease in entropy from ordering the cards is more than offset by the increase in entropy of the surrounding air. The total number of microstates for the entire system (cards + box + air) has increased, leading to a net increase in entropy. Irreversibility: This process is irreversible. You cannot simply "unshake" the box to return the air molecules to their original state and the cards to their disordered state. Local vs. global entropy: This scenario illustrates the difference between local and global entropy. Locally (just looking at the cards), entropy appears to decrease. Globally (considering the entire system), entropy increases. In conclusion, while the cards become more ordered, the energy input to the system causes a greater increase in disorder among the air molecules. The apparent contradiction between the ordered cards and increased entropy is resolved when we consider the entire system and understand entropy in terms of the total number of available microstates. This example highlights the importance of considering the entire system in thermodynamics and demonstrates how local decreases in entropy can occur within a system, even as the total entropy of the closed system increases, in accordance with the Second Law of Thermodynamics.
If the organised dice are basically identical it doesn't matter which position they take, it's essentially the same state, so low entropy. If they are disorganised it does matter which position they occupy resulting in more states = more entropy. It shows because you needed to put in energy by shaking/twisting to organise them.
Except there are not more possible configurations that the dice could occupy due to gravity. The dice can not float to those higher positions unless given energy by picking them up. Once packed they will stay packed in that configuration until acted on by an external force. I guess this is feasible in zero gravity but I’m not confident that would be the case.
because the systems volume stayed the same within the blocked u placed at 2:45, wouldnt the number of possible places for the die to be identical in both orientations? it seems like you just rearranged the dice while maintaining that the system's volume was equal in both cases (bounded by the stopper you inserted) Also, since the volume of space occupied by the dice in the new position was smaller wouldn't that also counter the point you are trying to make?
Great topic! I always learn something, realize how little I know about something and not understand something altogether in every episode, it’s awesome. Keep up the great work!
This is wrong. Entropy is the degree of unpredictability of a system. With the mixed up dice, you have two degrees of freedom - each die can be anywhere, and also can face any direction. With the neatly stacked dice you only have one degree of freedom: Every die can be anywhere as long as it fits into the predifined grid. The first has infinite posibilities, the second has afinite (elbeit very large) number of posibilities.
entropy is defined differently in different fields. your definition of it sounds like it would be useful in information theory, but i think he's using the definition used in thermodynamics. the entropy of an isolated system always increases as a result of irreversible processes, and i think this counts as an isolated system and an irreversible process.
I run a Precious Plastic recycling workspace, here in Italy, in my spare time. Usually I wash the plastic I collect in my washing machine (the european kind of, horizontal shaft), in a pillowcase, when doing laundry. Often I have some boxes with sliding covers, the ones that contain carbide lathe inserts, or telescopic boxes for drills, and so on. Sometimes I also have to wash bottle caps with child safety bottle caps (something from vaping fluids from friends and colleagues), made in two parts. I break the external part to separate them, and then put them in the pillowcase. Practically every time all of the parts come out from the washing machine re-assembled. It's amazing.
I have a feeling that if you balance on stilts, you have a single wave destructive interference counterfore to keep balanced. If your stilts have 1 pivotal joint, you need a second order countermovement to balance. A rubber band is like a stilt with billions of joints which will always angle to eachother in some degree. Even when you pull the band until break, there will still be some amplitude of angular movement. When the rubber band brakes and would shrink at lightspeed, the shape it had just before braking will be amplified. Like a roadtrain with 10 lorries waving around hitting a wall. If something is bent in the sligtest way, it will bend that way during impact. For rigid object like a broomsting it's a batlle beween compression stress and shear due to material ununiformity(weakest link).
In thermodynamics, we were taught that entropy is the amount of energy that is not available to do useful work. As such then, something that is not available cannot create a force. External work was done on the dice and nails to get them into the ordered pattern. They did not get that way by themselves.
Interesting fact is that with the most symmetric geometrical shape, the sphere, you cannot get entropy by shaking. This is because there are two ways of 'closest sphere packing' (cubic and hexagonal). Both packing structures will occur when you pile up balls/spheres and shake them. They will form random groups within the pile of spheres, and the bounderies between those groups will only get more defined the more you shake.
I gave ChatGPT your original question and it generated a similar answer to the one that you got, I then copied the transcript from this video give that as a prompt along with the instructions to read this and revise it answer, and it gave me the following: Based on the provided transcript from the video, the concept of entropy is clarified in a more nuanced way. Here’s a revised understanding: ### Revised Answer: Contrary to the intuitive notion that entropy is synonymous with disorder, the jar with the neatly stacked dice actually has **more** entropy compared to the jar with randomly oriented dice. This is due to the phenomenon of **directional entropic forces**. ### Explanation: 1. **Orientation vs. Translational Entropy**: - **Orientation**: When dice are randomly oriented, their orientation entropy is high. However, when they are neatly stacked, their orientation entropy decreases. - **Translational**: When dice are neatly stacked, they occupy less space, creating more free volume. This increase in free volume allows each die to have more positions it can potentially move to, increasing the translational entropy. 2. **Overall Entropy**: - While the orientation entropy decreases in the neatly stacked arrangement, this is offset by a significant increase in translational entropy. The increased free volume provides more possible states for the system, leading to an overall increase in entropy. 3. **Illustration with Dice**: - In a jar of randomly oriented dice, the dice take up more space and have less free volume, resulting in fewer possible states. - When the dice are neatly stacked, the packing is more efficient, and the increased free volume means more possible configurations for the dice, increasing the overall entropy. ### Conclusion: The entropy of a system is defined by the number of possible states it can be in. Neatly stacked dice create more free volume, increasing the number of possible translational states. Thus, the jar with neatly stacked dice has more entropy than the jar with randomly oriented dice. This reflects how entropy isn't merely about disorder but about the number of possible configurations or states of a system.
I always looked at entropy as the ending of something or decay but there's more to it. The heat death of the universe was the main example of entropy i had used to try to figure out what entropy is/does. Even in this video towards the beginning it seemed to me more like the tendency to even out, before you explained it more. So what I get from this is entropy is the tendency to or force of changing to a state of more potential from a state with less potential.
This video reminds me of my younger days back in the 90s. I used to prepare for raves by visiting a stimulating trader I knew. I was still young and naive and didn't understand why this friend would always take out a large bowl filled with dice and marbles. He explained that sometimes its not enough to hide the screwdriver. As my experience grew and I met different people I understood, Dude was just protecting his electronics with that bowl.
I'm skeptical that this video is correct. At 2:39, the amount of free volume per die has not changed at all; it is simply a different arrangement. There are, in fact, fewer possible states with the dice packed orderly than randomly. The dice stacked like that is the same as all of the air in a room being in just one half of it: it wouldn't be a stable state if there wasn't something else going on. What you have accomplished is more equivalent to a phase change, from an amorphous solid to a crystalline solid. The phase change is brought about by the loss of gravitational potential energy (as sound and heat) as the dice settle into lower positions. Yes, entropy of the system has increased, but no, entropy of the stacked dice themselves is not greater. This should be testable by performing the same experiment in a zero-g environment. I, unfortunately, lack the resources to go to space to perform the test. Any ISS astronauts here who want to play with dice?
You can still call entropy disorder, but just be careful of what you define as your system. For example, the dice ordering and leaving the volume has higher entropy, but if you were to consider the system as only the dices, and therefore don't consider that bit of volume that "creates" later, the entropy is lower. On a microscopic level it's easy to call entropy disorder, but on a macroscopic level defining systems is hard The example of the elastic band and the curled string of particles was really cool!
Please, someone correct me if Im wrong, but I understand that the order inside the Jar its only acquired after increasing entropy, because putting the dices inside the jar (a glass crafted with specific shape, proper to contain things in a certain way) it is already a anti-entropic movment... the entropy inside the jar its only coming to an aspect of order, because we are considering a closed system, ignoring that the jar was crafted in a certain shape (and also the dices), and separating therefore that closed environment from the total chaos of the universe.
This is more about the phase transition, not simply by entropy which should consider the free energy. Entropy is a part of free energy and phase transitioning to a more ordered system cannot be solely described by entropy. During the process, the entropy of the dice decreases by gravitational force and friction. Entropy is simply a number of possible states a system can have.
I won’t claim to be any expert, but I think the claim is that nature tends toward less organization. But an obvious exception is when an organizing force or energy is added to the system. For example you can separate ions using electricity or separate metals using magnetism, or separate different densities by gravity. In the case of the dice you have gravity and the shaking both acting toward the dice entering the lowest potential energy state, which happens to be more compact and ordered. If you shook the dice without any gravity, it would likely remain jumbled.
I was under the impression not that entropy was related to the total number of states, but the percentage of total states that contain an equivalent amount of information. There are a higher number of states where the dice are arranged essentially randomly than when they are packed. You also have more information density as to describe the position of the dice, you basically only need the diameter of the largest ring, the number of rings, the width of one doe, and the height of the stack. For the randomly oriented set, there's no way to predict the position and rotation of each die other than nothing down all quantities for all dice. Both of these would suggest the opposite entropic relationship (if my previous understanding of entropy was accurate... Which is not something I'm confident in)
2:30 is an interesting explanation, but I was just going with "gravitational potential energy" instead. As a thought experiment - if you were to repeat this experiment in a non-accelerating frame-of-reference, say on the ISS, would the dice self-organize too?
I love how your simple questions and demonstrations arouse the curiosity of so many. I never considered the entropy of a cup of dice before, for example.
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I love this subject, I liked it when I studied it too...
When entropy decreased we called that an open system, otherwise it was closed.
Like life on earth has a decreasing entropy. That's an open system. But when we take the sun and the energy that's coming from it the system will have an increasing entropy, now the system is closed...
Thank you very much for this. In calculations of steam engines, entropy is fairly simple. In theory, it leaves me repeatedly perplexed.
this is all good, but can I melt steel object by placing incredibly hot tungsten ball on it?
In the specific simulation you showed at 4 minutes the particles actually attract each other which is why it springs back. So the particles are pulled to the center of mass, but one end is anchored causing all particles to migrate left.
Notice the dice align from outside inward as they themselves mimic the shape of the cylinder in cylindrical layers
So all I have to do is spin my room?!
You spin your room right round baby right round
@@btd5311like a record baby right round round round...
Or i rock ur world
If it's in boxes yes, or shake it really hard if its spheres. 😁
Um should i spin the world?! Wait a minute... its already spinning... Wait what
I'm a physics student, and to my limited knowledge, the entropy of the dice did decrease.
But the process still happened because of the release of potential energy when a die falls.
The spontaneity may be determined by the change in the Gibbs free energy, which is given by dG = dQ - TdS (assuming isothermal and isobaric process). If dG < 0, the process is spontaneous.
This is because the increase of entropy of the surrounding (-dQ/T) compensates for the decrease of entropy of the system (dS), thus abiding by the second law of thermodynamics.
In this particular case presented in the video, since the system is not isolated (meaning, work and heat can trespass the boundary of the system), the decrease of entropy of the dice is compensated by the increase of entropy of surrounding caused by the release of heat that generated by the falling of the dice.
I genuinely enjoy every video of yours! Thanks for uploading such an amazing video :)
It seems a better explanation.
This makes intuitive sense. The demostrations in the video are wonderful to teach how crystals form: the particles slot in the position with the lowest bonding potential energy, in the same way as the dice and nails slot in the position with the lowest gravitational potential energy. Would you agree? (PS honest question: I'm a high school teacher who has to teach chemistry with a degree in botany 😅)
My understanding is that increases in entropy are increases in homogeneity. In other words, one subregion of a high-entropy region should be difficult or impossible to tell apart from an adjacent subregion with the same level of entropy. To me, that sounds like a crystal lattice. The term "order" was, IMO, originally slightly misused when the terminology for talking about entropy was getting established, since some of the physical effects of increased entropy are at odds with our natural language use of the term "order" (and its inverse, disorder) to refer to things like how tidy your room is, or how regular a printed pattern is.
@@Mikee512 the third principle of thermodynamics can be stated as "a perfect crystal at 0K has 0 entropy", which to me seems at odds with this interpretation. A perfect crystal would be perfectly homogeneous, with each region indistinguishable from any other, corresponding to a single microstate. Am I wrong? 🤔
So you're saying falling dice are hot?
Another thing to consider
The dice and nails also reached a state where the gravitational potential energy of the system was minimized, the disordered arrangement took up more volume meaning there were lower states the dice could be in if organized.
The gravitational potential energy was thus, dissipated as sound and heat.
This is equivalent to the nature of living systems. They exist in what we would call a more ordered state, but their capacity for converting useful forms of energy to waste heat more than offsets any apparent decrease in any other aspect of entropy they cause.
Reading that made my living system fart.
@@cosmicraysshotsintothelight doing your doody
Seems work was done on the system with the twisting torque input or shaking the nail box. That kinetic energy converted to waste sound/heat means entropy increases. Gravity is another static input to the system.
I think this might be the main reason they align.
@@H0A0B123 Shimmy Shimmy Ko Ko Bop!
Gotta disagree with the reasoning that there is more entropy in the ordered dice because they are more compact and "have more room to move around." They only have more room compared to the height of the disordered state. The dice are not actually concerned about the height of the disordered state, so I would argue that they are in fact at lower entropy since the room they care about (to the sides and below them due to gravity), is less, and there are fewer opportunities for the dice to move around.
I think this is true if you only look at the dice. But we are looking at and comparing the system in a packed state vs a random orientation state. When looking at the system as a whole we must keep the volumes the same.
Yeah.
Entropie relates to the number of microscopic states that have the same macroscopic properties.
The ordered dice have lower entropy since there are fewer such ordered states than unordered states (roughly, you can orient an ordered die in 24 ways, an unordered one in many more ways).
The fact that the system spontaneously becomes ordered does not mean that that order has higher entropy.
This is incorrect. When the dice are disordered, many of them are effectively jammed and can't move at all. On the other hand, when the dice are ordered, each dice is free to move a little bit. They don't have much room, but remember that entropy is related to the number of possible microstates. It increases with the factorial of the number of dice when they can all move.
Entropy-driven crystallization is an entire field of study. It's really counter-intuitive, but the explanation in this video is correct.
@@cwpeterson87 Dice don't have to move for entropy calculations; moreover, if they are well packed they would also not move. That is a red herring imho. I could for instance swap dice (even if they are blocked, I can still imagine two states that differ by a swap); thát gives multiple microstates with the same macrostate. Similar other processes like that.
Most compelling to me is that this is completely analogous to crystallisation, and a crystal has lower entropy than - say - the corresponding gas.
There are lots of other effects here. Like, the dice fall down, thus decrease in gravitational energy, which energy is dissipated such that the dice warm up. And thát heating still increases entropy in compensation. (They release heat, just like crystallisation does btw.)
The argument in the video that the packed dice have air above them to move to is not correct either in my view: it requires energy for dice to move up there against gravity, so that is no longer the same macrostate; it has different total energy. (And on top of that, the jumbled dice leave exactly the same room for air among each other.)
The dice aren't "concerned" with anything because they're inanimate 😂
Does entropy also explain why elementary school students never line up in a straight line?
Did you try shaking them?
Random and chaotic.
Bro…it might.
I was really just thinking about what implications this phenomena has on living organism behavior, not just these inanimate objects that are being observed for the video
@@juroph7😂
Excellent video, but I think you have it wrong with regard to the dice and nails. They settle when jostled into the lowest energy state - that being the lowest overall point in the gravitational field they are in. Do the same thing in a location without gravity and you'll get different results.
I agree with the rubber band example however. Note that stretching a rubber band heats up the rubber, and it cools again when it contracts. This is consistent with entropy. The nails and dice would also heat up (or increase in average speed) if you jostled them in zero gravity just like the rubber by the amount of energy expended to jostle/stretch.
Entropy is simply a measure of how likely a configuration is. Sure, it's possible that rubber band could stretch itself just sitting on my desk, but with 100's of billions of molecules in it all needing to do essentially the same thing at the same time over a long period of time (contextually speaking) a mathematician would call it a statistical impossibility.
I'm not sure about the rubber band one personnally, and if their is a contribution the force produced would be almost nothing compared to the intra and inter molecular force involved in an elastic.
@knurlgnar24 Agreed, Action Lab reversed the scale conventionally used to measure entropy. The disordered box of nails should be said to have relatively higher entropy than the more ordered box. I stopped watching after that botched intro.
I think if whoever the first person to use the word "disordered" to dscribe entropy had instead used "homogenous" or something I think we'd be like 50 years ahead with our understanding of physics and information theory
entropy was devised before we even knew there were atoms. they had some "energy available to work" thing going on.
Doesn't work either : case in point oil does not mix with water, and homogeneous emulsions separate into distinct layers.
The first use of entropy came from the observation that heat transferts spontaneously goes from hot stuff to cold stuff, and that this puts a hard limit on how efficient a thermal engine can be.
The modern understanding of entropy is that it is a measure of the number of microscopic states a system can be in based on the values of observables that can be measured at our scale.
The channel alphaphoenix made a really good video recently if you want a more in depth explanation.
"homogenous" is closer but not quite right. I think "likelihood" is a better description but still not perfect. If you allow a system to evolve undisturbed for an arbitrarily long amount of time, taking observations at random times, higher entropy states are more likely to be observed over time.
To me the best description of entropy is it’s the act of something reaching its most stable state. Like with these dice being organized like that the dice is more stable than when they are disorganized. Rust is chemically more stable than iron.
Yeah a splattering of blue and red paint has less entropy than a smooth coating of purple paint (or however the paint combines)
2:35 sounds fishy... please check:
1. microstates in the Bolzmann formula have the same energy. Here, if any dice goes to the free space above, the system will have its energy increased by the work against gravity. This breaks the condition of the microcanonical ensemble
2. Microstates are equally possible, however we don't see dices jump into the free space by their own will, therefore the shown state has much larger probability to be in and this breaks the condition of the microcanonical ensemble
I agree with your description, but bear in mind that this system wouldn't be described by a microcanonical ensemble, because it is not isolated. In fact, Boltzmann entropy would not be the correct expression for entropy in this case I reckon.
This looks more like a (N, g, T) ensemble, where available states are definitely not iso-energetic. Further thought is necessary on my part
@@andreacosta7712I guess you've meant canonical NVT ensemble. I agree with you, it should be more suitable in this case. However, I played along with the author, who decided not to introduce Gibb's formula. However even if the energy distribution of microstates was considered, my point (2) would still hold.
I actually try to lead to an idea that the author has some sense in his words only if he never stops shaking the jar and even in this case it could be hard to say smth specific about energy distribution of states and the resulting entropy
Definitely, any kind of thermodynamical reasoning only holds if the shaking is ongoing, aka constant temperature.
What I meant was indeed NgT. Volume is not constant, but gravity is. In a way, a constant-force ensemble is equivalent to a constant-pressure one, as in NpT, which is described by Gibbs free energy.
My general point is that in this demo, the interplay of energy and entropy is what actually explains the phenomenon, so reasoning in a microcanonical framework does not give you the full picture, because entropy is constant in it. But yes, point 2) still holds.
🤭im not smart enought to understand
@@JackAtlassBasically, these are bad examples using the wrong math, failing to state the things he wants to state even though what he's saying is true. He's wrong in every step of explaining why it's true.
This is a wrong explanation.
The spontaneous orderly arrangement in the example is due to the effect of gravity. Dice can lower their overall center of gravity when arranged neatly, and the same is true for nails. If gravity is removed, such as by astronauts conducting experiments in the space station, you will see that neither the dice nor the nails will spontaneously organize neatly.
In the animation the Gravity is switched off so you have a point.
@@andymouse Maybe It approximates the dark matter flowing over and through us. Galaxies start out as ring galaxies and "acquire" arms and bars and get warped along their rotational equator and things due to perturbations from other stimulus. An in space simulation would be all the dice in the cylinder in a random meander. Similar to a space containing a gas. It would take longer than it takes for tar to drip to get the data.
But if you remove the gravity of Earth or any other massive object the dice themselves would still gravitationally attract each other and they would form a clump with mostly face to face contact, very similar to the way they are arranging in the bottom of the tube.
Shaking in combination with gravity, yes.
@@aSphericalCow618 It's shaking plus gravity. Otherwise they sit as at start of video, further apart and unoriented.
Now try the same experiment without gravity pulling all items into the same direction.
Entropy is a function of gravity
No, it is actually only a function of the number of possible states. Just check the Boltzmann equation
'Amount of free volume per dice increases'. I thought that the amount of free volume is the same before and after aligning dice in a finite system, it is just that the same 'old' free volume is now concentrated in 'new' free volume in space continuously, above the dice, not scattered between dice.
You are correct
yep - If we follow this guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same.
(If we are allowed to reduce the volume in the ordered dice system, Then it has lower entropy.)
Yep, exactly. Though my chemist heart immediately made me instinctively want to say ‘surface tension’😂
Yep
Ehy, I haven't checked the entropy calculations for the dice problem, but I have the feeling that the problem can be formalized in a way to define a free energy (akin to Gibbs free energy for chemical systems at conatan p and Helmoltz free energy at constant V) for the system as a combination of entropic effects and energetic effects. The energy in this case is given by the gravitational field and the constraints of the jar. If you had the same jar (with a lid, to make things simpler) in space, the average equilibrium state would be the one with the disordered dice scattered all over the place. I think that the only reason why you reach the ordered configuration with your shaking process is because that configuration corresponds to the local minimum of free energy for the system in the gravitational field. The shaking is just a way to go from local minimum to local minimum until you have reached the global minimum.
The fact that the equilibrium of systems subject to forces is not the maximum of entropy is a well known fact in chemical thermodynamics. In fact, almost always, maximizing the entropy doesn't give you the chemical equilibrium of a system. Otherwise you could not explain things like the formation fo crystals or even molecules at all.
The second principle of TD tells you that entropy is a thermodynamic potential only strictly for isolated systems: for all other systems, you need to find a suitable TD potential to minimize or maximize given the constraints of the system. The only thing that TD (specifically, non equilibrium TD) tells you about entropy is that any irreversible process comes with a positive entropy PRODUCTION (not entropy): but for any non-isolated system, you can always let entropy in and out of the system by suitable fluxes of heat or mass.
Finally, I am sure you are familiar with the fact that since Boltzmann's pioneering work on the statistical interpretation of entropy, there have been several different definitions of "entropy" related to microstates of the system, more or less coherent with each other and the classic definition of entropy proposed by Clausius. Even without entering the rat's nest of which statistical definition of entropy you are referring to, I would honestly be surprised if you cannot find a coherent formalism in terms of free energy to describe the entropy of the dice so that it indeed decreases as it approaches final metastable configuration, thus attributing the driving force to an energetic factor.
I gravitate towards your answer as the best one. 👍
To my understanding entropy describes particles "desire" to reduce their energy to reach the most stable state. The dice prefer the tightly packed state because here they have the lowest amount of potential energy. Also it takes a lot more energy to break that state apart, because the previous unorganized state could be broken apart by the tapping / rotating, the new state however is hardly affected by it.
Indeed. When you have packed particles, if you free them on a bigger room, they redistribute to reduce their energy. On the dice scenario, this happens also for reduce their energy.
isn't that enthalpy?
That is enthalpy. Entropy is simply disorder.
Nice video, but Entropy in the original statistical mechanics sense of S=log(Omega) is good assumption ONLY in an energy conserving equilibrium system, what is generally called a microcanonical condition. In the case of macroscopic spheres (or dice) you have a dissipative system in which a lot of energy is dissipated into heat during collision and this is why you have to provide energy by vibration. This is a steady state and not an equilibrium one and entropy technically is not defined. Clearly you can use the dice example for pedagogical reason, but with a bit of care. You said: "any system wants to maximize entropy" this is not true. Let me give an exanple. If you wold have a mixture of two macroscopic spheres in a shaker they will have a strong tendency to demix with the big spheres going on the top (brazilian nuts effect). In a equilibrium system this will be nuch more unlikely (especially if rhe sizs ratio of the two spheres is not too large) because mixing increase the number of condigurations and consequently entropy.
This is what I couldn't understand when I was watching it... "aren't you putting energy into the system when you shake it?"
The trick here is not to compare the original disordered dice configuration to the final ordered one, but rather to imagine the distribution of dice orientations while the container is being shaken. At equilibrium, most of the dice align and the ones near the top are constantly and rapidly bouncing around.
If the container is not being shaken, the entropy of both configurations near zero because the dice have almost no probability of changing state. And analyzing the situation becomes harder because the disordered configuration will have a higher energy level due to potential energy than the ordered configuration
This is true but a more practical role would involve calculating the partition function. We need to incorporate positional and configurational entropy due to the limited volume. This would be more a more detailed approach and would incorporate both positional and potential energy considerations.
If we replaced the dice with smaller particles like those Einstein first observed brownian motion in, it seems clear the unpacked disorganized dice are much higher entropy. Random disturbances are much more likely to lead to an unpacked vs packed state. For every 1 packed permutation, an enormous number of translated identical ones. Am I missing something?
So the few at the top have more entropy but most are trapped in the structure and have less.
3:33 This is semantically untrue. The reason the rubber band returns to an unstretched state is because of electrostatic attraction and repulsion between the molecules within the rubber, which respectively resist stretching and compression, and thus effectively function as an elastic force. You can explain this as a mechanism that acts to increase entropy, but this does not change the fact that the force is elastic in nature.
How does that argument account for the temperature dependence of E?
They all align expect for that CHAD nail at the bottom 0:57 seconds
Sigma nail behaviour
Sheeples. am I right?
Very based. "I don't conform to your laws of physics, you science bitch!" - Nail Chad.
I'm nothing like yall 😎
that was actually just a nail like object
2:54 would have been a good idea to start the video with “entropy is defined as”
Yeah Totally agree 😂
The ordered jar has less entropy, with the dice compacted there is less positions they can actually occupy while still looking the same in buik; but the total entropy of the Universe increased with the heat of the friction and collisions though. Just like life, we may seem to violate the laws of thermodynamics with all our growing and reproducing, but it's actually the opposite, we spread heat more easily than still rocks.
The story of the dice themselves decreased, but the entropy inside the jar as a whole increased as a result by compacting the volume. Honestly though, he is using semantics.
That's incorrect, energy neither increases or decrease, the universe is moving towards the most statistically likely configuration which is the true definition of entropy.
*The 3 levels of entropy from less correct to more correct*
1: A system moving in the direction of a more disorderly state
2: A system moving towards a state of equilibrium
3: Energy and matter displaying the most statistically likely configurations
*Creating the arrow of time by moving towards that given configuration that can be more or less statistically likely but the ones which are the most likely are considered entropy
@@notaffiliatedwith7363It's not about geometry and order, it's about the most likely configuration in a given system with it's laws of physics at work
@@markmuller7962 Yep, "order" and "disorder" are subjective, so they do not always match with the entropy. A good example is oil and water separating over time when with most other liquids we see the opposite.
@@jacobblaustein7779If the jar entropy has been increased, it's due to the heating while wildly shaking. The jar is not a closed system. Explanation is not valid, or not complete, while heat and sound noise are not considered, as well as random shaking.
What was said in the beginning of the video, that the 'ordered' systems (dice or spheres) have more entropy than the disordered ones is not correct (if we look at the isolated entropy of the packing of dices and spheres). You might consider correcting this.
These systems do not reach a state of maximum entropy, but the minimum of an energy potential (like the Gibbs potential in thermodynamics). For the dices and the spheres this potential contains a gravitational energy term, which is the +m*g*h, where m is the total mass of the dices or spheres, g the gravitational constant and h the height of the center of mass of all the objects in question. The second term is an entropic one -c*S (c is some constant depending on the thermal energy or the shaking intensity in this case). The system now tends to adopt a configuration of minimum m*g*h-c*S. The close packing reduces h and this term dominates and therefore the dices or spheres adopt a packing where h is smallest possible even if S is not at its maximum. Here minimal h and maximum S can not be reached simultaneously.
To understand this consider there is no gravity (i.e. g=0) then only the entropic term -c*S is left in the potential and the system will adopt the state of maximum entropy (i.e. all dices and sphere floating randomly in the cylinder) at the mildest shaking (i.e. c is not zero). The second case is strong continued shaking. In this case c will be very large and m*g*h will become negligible (basically g can be assumed to be 0). Then again the dices and spheres will ‘float’ randomly in the cylinder due to the shaking.
If he said 'maximum entropy' then he's wrong on that as you say. He's also mixed up on another count i'd say: If we follow the guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same.
(If we are allowed to reduce the volume in the ordered dice system, Then it has lower entropy.)
Reminds me of how the initial state of the early universe would have appeared about as random/disordered as possible yet gravitationally speaking was very low entropy.
You’re living in a dream world neo.
Much ❤ Love
🌎🌏🌍☯️⚡️
World🌞Peace
but it's hot af.
The initial state of the universe is extremely ordered. All matter existing in the same point. There is only one configuration for that to be the case.
@@JamesDevlin-d4z It wasn't a single point. The universe before the big bang was still infinitely large, it was just much, much more tightly packed. At least, according to the widely accepted theories.
In the beginning God created the heaven and the earth.
I'm joining team "I don't agree".
Because the dice in the ordered state have fewer opportunities to change position. If you keep doing that start stop they no longer move. Where in the disordered state they do move. Meaning the disordered state has more opportunities for the dice to move and therefor a higher level of entropy.
1:30 most people dont know what entropy is at all though
One way to clarify what he's talking about is if you understand entropy as hidden information rather than disorder (the latter of which I despise as an explanation of entropy). In this sense, free space has no information content, amd thus no hidden information. By lowering the average free space in the local vicinity of the dice, we are hiding more information, because now any given die could have any 6 other die (or 5, if it's against a wall) directly pressing up against it. This is the massive increase in translational entropy that he's referring to.
Ah entropy, the 3rd wheel of thermodynamics
three wheel bicycle. 😂
Third wheel is what makes it a tricycle
More like a fifth wheel you know the company nobody wants around 🤣
Quite the opposite. It helps you so much to find properties of many Systems.
Ah
This is not entirely correct and in fact could be incorrect. It’s not black and white. We have to keep this simple and not try to manipulate individual concepts but instead focus on the combined perspective.
Configurational entropy and positional entropy both need to be considered and calculated. If the extent of free volume significantly affects the number of Microstates that are accessible, then it’s possible the organized dice may have more entropy due to positional freedom. If the volume is more constrained, randomly orientated dice will have more entropy. We can not make the claim that one has more than the other without proper measurement.
If we follow this guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same.
(If we are allowws to reduce the volume in the ordered dice system, Then it has lower entropy.)
*The 3 levels of entropy from less correct to more correct*
1: A system moving in the direction of a more disorderly state
2: A system moving towards a state of equilibrium
3: Energy and matter displaying the most statistically likely configurations
*Creating the arrow of time by moving towards that given configuration that can be more or less statistically likely but the ones which are the most likely are considered entropy
(3) need a tweak: the whole point is that all microscopic configurations are equally statistically likely (at the same energy), but there are just so many more with the "right" macroscopic variables that it always looks right.
e.g., the configuration of N2 and O2 molecules in the room (all your rooms) right now has the same likelyhood as the one with all O2 on the left side and all N2 on the right side, but there is only one state that looks like the latter, and more than Avagadro's number to the sixth factorial that look like the former, and (N_A^6)! >>>>>>>>>>>>>>> 1.
The "arrow of time" is not necessarily a more correct part of your difinition. An interesting idea, but not demonstrable. Sean Carroll (the physicist who proposed this) is a *theoretical* physicist and his idea arguably enters into an unprovable area.
@@PsymonHawkeye Actually the arrow of time is a side addition to the third concept just to make it clearer. And btw it's not a matter of hypothesis, the main role of entropy in the arrow of time is a theoretical physics *fact* aka scientific theory which doesn't have anything to do with the English popular use of "theory". It's a scientific theory, learn how science works
@@DrDeuteron Yes everything is emergence but the definition was getting too long already for a YT comment
@@markmuller7962 agreed. Idk, that was my favorite part of statistical mechanics.
I use it to disused lottery players:
Me: “ you should pick 1,2,3,4,5,6”
Them: “why? That will never come up!”
Me: “exactly.”
I always understood entropy as the drive towards a stable state where no work is done, e.g. when all heat is evenly distributed in the universe, there is no transfer of energy (because heat doesn't pass from cooler to hotter (thank-you to Flanders and Swan for their song about the laws of thermodynamics) and everything is equally hot. The dice stop moving once they are aligned because the are then at their most stable configuration. In an earthquake, things fall down because being on the floor is their most stable state.
Hey! I like your video, but I have to ask for clarity. You treated the bowl of dice as a closed system while exerting outside forces. I believe you when you say the total entropy of the final system (inside the bowl only) increased, and the entropy of the drill also increased. Why was the outside force ignored? In another system where outside forces are ignored you may have decreases in entropy. But missing the outside force leaves the question open, does the entropy decrease in the bowl balanced by the entropy increase in the drill? Of course you explained that when looking at possible states it is favorable to pack. Further, thanks for the video, we fail to remember that "ordered" is a human imposed concept, if we define it as the low entropy states, then the bowl of none packed dice is more ordered than the packed one. But our brains like to call the packed state as more ordered.
As an aside, regarding "ordered" being a human imposed concept, I tend to think of "order" vs. disorder being recognizable patterns vs. a lack of recognizable patterns. Of course taking macro and micro into account, there are patterns that we don't always immediately recognize as such. You can quickly get into "does a tree falling in the woods make a sound if there's no one there to hear it" territory (we know the answer to that of course). Referring to whether patterns/order requires observation to be considered patterns/order vs. random chaos. The science of the impact or lack thereof of observastion of phenomena in the universe continues to be intriguing topic.
I'm confused. The number of configurations of the ordered state is smaller because the number of possible configurations is limited to permutations of the dice with their neighbors. As opposed to the disordered system, where they can permute with their neighbors as well as form various other random disordered configurations largely indistinguishable from the particular state this system happened to be in before you did work to it. What am I missing?
Is this a feature of being in a central force field? The fact that the potential energy of the system as a whole is higher if it has dice are at a higher level, and the "relaxation" of this system to a lower energy state is the key? This is how I see it differs from the box example where the lower energy state is the even mixing. We needed to do work to put them in the corner, since their tendency is to NOT be in the corner. This is reversed here due to gravity even though you had to do work to the system by shaking it to order them.
Which scientific articles or books were used in the video?
He made it the F--- UP!
They're in the description
My understanding is that the jar with the dice packs in an ordered way because that decreases the total gravitational potential energy of the dice, which makes that state more likely. If jar were in a state of weightlessness, the disorganised state would be more likely.
0:10 As ITALIAN i recognise the “why”😂
🤌
The second law of thermodynamics applies to closed systems, not all systems in the universe, nor all theoretically possible universes... But an interesting video that will be fun to think about.
Free volume is not created. The many random small amounts of volume have been combined into one larger volume but no extra has been added.
THIS.
yep - If we follow this guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same.
(If we are allowed to reduce the volume in the ordered dice system, Then it has lower entropy.)
My thermodynamics professor had something he repeated constantly, "now we just count the states." Right, "just". The text (which he wrote and distributed free) had an explanation of how we knew all the states had been counted. Entropy was simple, the more states possible the higher the entropy and the more probable that the system would be in one of those states. Amazingly most of the laws of gases, liquids and even solids could be reduced from this "simple" counting of states.
I'm not going to attempt counting the states of dice in random vs. ordered configurations but I'm pretty sure that from this perspective there are more states of randomly ordered dice.
My lesson I learned is that the properties which apply to atomic level particles are not necessarily those that apply to macro sized objects.
Except with the disordered dice the volume is largely inaccessible because each open volume is less than the size of a die.
@@JK_Vermont Not the issue. The video was claiming that volume was created. Not that usable volume was created or more useful volume was created. Details matter. "It's physics for Godsakes".
I saw it differently. The random dice in the glass has a higher potential energy state than the organized stacked state hence the jiggling tends to organize the dice.
Now I don't understand entropy.
😂
Basically the smart way of saying disorder or mess
@@nonabroladze8203 no it's not mess or disorder. they are just the more probable outcomes. it just mesures the number of arrangements particles can have(it have more to do with the distribution of energy rather than particles) . a cube of ice have almost one arrangement of atoms while vapor can have an astronomical amount of arrangements. vapor got more entropy than a cube of ice it's not about disorder. disorder just tend to corelate with it in most cases.
@@nonabroladze8203 as the guy showed in the video there are more ways to arrange the dice in an "ordered" maner than there are to arrange it in a disordered manner even if the entropy is high the cube arrangement will get more ordered with time.
@azouitinesaad3856 ty
I read in a book that way and that's how I knew it😅
I prefer to think of entropy as pointing in the direction of the arrow of time - jiggling and jostling over time will tend to produce the most common configurations. This only holds if all configurations are equally available and aren't sticky. Natural filters in life put a non-random bias against this jostling, from your example here to the gravity wells of stars and the motion of beaches, or Life's Ratchet in the cellular machinery. If once a random state occurs that locks in a position (like your orderly dice that can no longer move) then they will tend to order up even if order up states are less common, because they stick. No matter how slow the decay is or how uncommon the state of a random decay is, Schrodinger's cat will die when it happens and will stay dead (cat will randomly die but not randomly resurrect), so over long time you are much more likely to find a dead cat than a live one. Entropy was meant to describe states that are fully free to interact in the system, not natural filters. It doesn't break physics, it just doesn't fit that model.
If you think of entropy not as of particle concentration or arrangement, but as the most likely outcomes over long times scale including non-random natural filters, then a compact star or beautifully orderly beach sand are actually low entropy as the dead end of the jostling options. This kind of one-way-ness also applies in other realms like gambling - where no matter how much you win you still can still risk all and lose all, but once you are broke you cannot un-lose. The house always wins even if you have slightly favorable odds, because even a less common disaster cannot be recovered while all cumulative success is just one bad roll from being wiped away.
1:10 gravity, the pieces want to be at the lowest point possible so they pack together to make them as low as possible
Entropy? :D
This is more about a constant field of gravity acting on the contents locking them in place, and the constant work input by agitation that allows each die/bead to move out of its current local minima and fall into its new place. Once slotted into positions, gravity and force from their neighbors restrict them from moving out of place. This effectively locks them in place. It just so happens that the most 'restrictive' spaces are also the most space-efficient structures (highest packing efficiency), and crystalline structures are quite space-efficient.
Hence spheres forming a face-centered cubic instead of body-centered cubic or other patterns.
Given the magnitude of forces at play, they drown out any entropy changes you see in the system.
Try doing this test without agitation and gravity messing with the system. Try suspending them in solution of similar density. If you let the solution evaporate or drain slowly, it might shed a decent light on crystal formation too. (drain too fast and they will look more disordered, and 'crumbly' too) :D
Cool video! I have seen many confusing explanations of entropy, but on of the better ones is "Entropy states 'that which is most probable will probably happen.'" In a random system, the probabilities reflect that in disorder. If the rules of the system are ordered, the result will generally be ordered. In application it's a little more complicated than that, but in general essence it seems to be right. So I guess the entropic force is the tendency of the system to align to its underlying probabilities.
Which simulation software at around 4:00?
I also want to know this
1:45 Well Said Remember Folks, AI will give you the Popular Answer, not Necessarily the Correct Answer.
[Usually Popular = Correct AND you also want to Double Check some other way]
As others have already pointed out, gravity is also driving this process. When the blocks align with each other the overall center of mass is lower, so it's a lower energy state.
It would be nice to test this in a zero G environment, but since those are hard to come by, I'll offer an alternative. If you can fabricate blocks of neutral buoyancy, the experiment could be repeated underwater. That would eliminate any effect of gravitational potential energy.
It would be interesting to see the results.
"When enough chaotic and random events happens. Eventually, it leads to very predictable events."
Thats quite philosophical. So after enough observations, everything will be understood.
We are imperfect to understand all. Only God knows.
Yet the definition of chaotic and random preclude the possibility of predicting. So are the events truly chaotic or random? If they are predictable then they can't be.
@@PhokenKuul No, not if you are part of the system being analyzed yourself eg human nature.
@@PhokenKuul Made me realize that i find it philosophical because of how paradoxical it is.
@@PhokenKuulthis is incorrect. There is nothing in the definitions of chaotic or random that preclude prediction. Dice rolls are random but I can accurately predict that each number will appear 1/6th of the time in a large number of rolls.
There are a couple things that don't make sense to me about this. And these aren't rhetorical questions, I absolutely believe your account of how it works since you know much more about it than I do. These are points of genuine and self-acknowledged confusion.
1) If entropy depends on number of possible configurations, shouldn't the dice still have higher entropy when more disordered? You say they have higher entropy when tightly packed because there's more free volume above them, but it seems to me the number of possible configurations of the dice is higher the more volume the dice _do_ occupy, not the more volume they _don't_ occupy. I realize the dice are actually separate objects, but if we think of the volume they occupy as this connected, amorphous cloud, then shouldn't there be more possible places we could find any given die in the larger _that cloud_ is, _not_ the larger the _air above it_ is? I guess what I'm getting at is, if we consider only the configurations where the dice are tightly packed, it seems to me the probability of finding any dice in the unoccupied volume above the dice, that volume you described as "free," is by definition _zero._
2) Also, generally, how valid is it, really, to discuss entropy as a number of _possible_ configurations of a system which has a _known fixed_ configuration if closely observed? If die A _is_ at position P, and die B _is_ at position Q, then the probability of finding die A at position Q or die B at position P is zero. I know I just got through saying we can think of the occupied volume of the dice as this connected, amorphous cloud, but can we really? Isn't that occupied volume actually a precise crystal structure in the exact shape of a whole bunch of cubes, with pockets between them excluded from the manifold? By that logic, it seems to me that _everything_ has zero entropy at all times. I realize this notion of exact knowability doesn't hold at a quantum scale, where the uncertainty principles take effect, but we aren't _at_ that scale.
Every time I'm pretty sure I have a solid understanding of entropy, something comes along to prove me wrong! Nicely done.
This really changed my understand of entropy and appreciate the perspective that life is an emergent property of a system that has evolved to increase entropy while efficiently dissipating energy. The variety of life on Earth shows that a relatively small number of different chemical elements can assume quite a variety of arrangements. Carbon is entropy's strongest proponent in that realm.
I feel like I've been brainwashed
Action Lab reversed the scale conventionally used to measure entropy. The disordered box of nails should be said to have relatively higher entropy than the more ordered box.
he's wrong - If we follow this guy's process and keep the volumes of the two systems (1/higgly-piggle dice and 2/ordered dice) constant then what he shows us (higgle-piggle / ordered) each represents a single microstate/config of the same macrostate. Both systems can reach all the other's possible microstates given some input of energy. They have the same number of possible microstates and the same macro. The entropy of both systems is the same.
(If we are allowed to reduce the volume in the ordered dice system, Then it has lower entropy.)
AL is an idiot.
I'm not an expert on entropy, but the easier explanation in my mind is that the aligned dice simply have more possible states available. Consider 100 dice stacked in the bottom of the container - each cube can be swapped for any other so you have a total of 100! possible states. Now imagine that 20 of them are sitting on the edge - each of the cubes lying flat can be swapped with each other flat cube (80! possible states), and each on-edge cube can be swapped with each other on-edge cube (20! possible states). So the mixed orientation configuration has 80! x 20! possible states which is SIGNIFICANTLY fewer states and therefore lower entropy. Adding additional orientations here lowers the entropy. (Yes, this is a simplification of the situation)
I'm not yet totally convinced that the "free volume" concept is very helpful in understanding the increase in entropy with the dice here even though the difference in volume will certainly play a role in the number of states.
Although it's pretty surprising, I wouldn't say there is anything "mysterious" about this "force". Where there are MANY more possible ways for a system to do something, the system will tend to eventually do that thing. At least, that's how I like to think about it.
(0:02) Let me guess... You bought a cheap bag of D6 dice that needed to have their dots filled in with a marker. 😉
Why else would you need a 💯 dice anyways.
I watch tour channel mainly for how you make science topics fun and engaging with clever and novel experiments, but then every so often you deliver powerful insights expressed really intuitively and clearly. Thank you. Excellent work.
When you jostle the dice, their gravitational potential energy is being dissipated as sound and heat, so they tend towards a "ground state" where their potential energy is minimized (by being packed as low as possible). The entropy of the dice does indeed decrease because there is only one "ground state" (up to rotation of each layer). It's possible for the dice's entropy to decrease because they are not a closed system - you are not counting the microscopic degrees of freedom where the sound and heat end up as part of the system, and if you did, total entropy would increase.
Another way of looking at it is if there were no energy dissipation into those microscopic degrees of freedom, then the dice collisions would be perfectly elastic and they would keep bouncing around instead of settling.
Greetings from Slovakia
I've quite recently finished writing my PhD thesis on entropic phase transitions in some specific systems. I have a whole section of a chapter devoted to "trading" one type of entropy for another type for a net entropic gain. I find this phenomenon very fascinating and almost each one of my scientific papers has a short, "intuitive" discussion how it is applied to the case on hand.
Since when does ChatGPT "represent most people"? STEM bros really crumble at the thought of social research, huh? You could've easily made a poll of your audience or cited popular definitions of entropy in recognized dictionaries but you chose the laziest way possible, somehow equating an LLM with "most people" as if it's a fact.
While the entropic force is a major factor in a rubber band's retraction, it's not the sole force at play. There are also:
Enthalpic Forces: These arise from changes in the internal energy of the rubber band when stretched. Stretching stores energy in the polymer bonds, and releasing the band allows this energy to dissipate.
Cross-linking: The polymer chains in rubber are often cross-linked, creating a network that resists deformation. This contributes to the overall restoring force.
The Dominant Force:
In most everyday situations, the entropic force is the dominant factor in a rubber band's behavior. This is why heating a rubber band (increasing entropy) causes it to contract, and cooling it (decreasing entropy) makes it stretchier.
Important Note: The balance between entropic and enthalpic forces can change under extreme conditions (e.g., very high or low temperatures) or with different types of rubber.
In summary: The entropic force is a significant factor in a rubber band's tendency to return to its relaxed state, but it's not the only force involved. Enthalpic forces and cross-linking also play a role, although their contribution is usually smaller in typical scenarios.
Good Morning!😃
I saw your journey on the Alan Pan video recently, and watched some of your content after. you should do more TH-cam videos
This is why science is so great. Its about studying whats actually going on regardless of preconceived ideas or beliefs. Properties of the Universe can get confusing (especially when there are multiple things going on and many variables). Science is studying each one, recording data, repeating, recording, etc.
Humans love to see one event and assume they know everything from it...we know thats not the best way yet here we are in 2024 with 10s of millions who would rather believe what they want to more than what is real.
Your videos make every hard concept seem so fun and easy
You have to be careful when talking about the entropy of one specific system with respect to another. Entropy can only be defined for an ensemble of systems that satisfy certain conditions. In the case of the cubes that are "axis-aligned" rather than with random orientations, does your ensemble include states where the cubes are floating in the extra air space you describe -- or does your ensemble only include microstates that are stable under gravity? If you only consider microstates that are stable under gravity, the extra volume gained will not be occupied by stable states. Hence, the "axis-aligned" system would seem to me to have less entropy, as our intuition would tell us.
Furthermore, if we are to use the fact that all microstates are equally likely, it would make sense to limit our ensembles to "stationary states" that have long lifetime -- not states where die are momentarily in the air occupying that extra volume.
If someone has a different interpretation or thinks I'm wrong in some way please let me know!
Once the universe reaches full entropy, if ever, that will be perfect order. Or as close as you can get to it. How people come to the conclusion that entropy is chaos is beyond me
I think the way that communicates best how I understood entropy is "The inverse deviation from an object's state at the end of time," meaning, the more entropy increases, the more closely an object will reflect the state it would be in as time approaches infinity, and that entropy is used as a way to gauge how far away an object is in an initial state from the state it will reach at the end of time
4:07 you say there's no forces acting on the particles making them coil together but actually in the simulator you used the electromagnetic force is simulated, which is what's pulling them together
Finally someone who gets it and can actually explain it in a good way.. Damn, not even my university profs got the concept of entropy! The whole "you can't unmix the marbles!" and other demonstrations of randomness to explain entropy completely ruined the idea in the public mind. We need more of these videos!
2:09 you lost me
I got inspired to ask Gemini (my old friend) and it gave a similar answer to Chat GPT, so I fed it the transcript for this video, and Gemini agreed, so we concocted a question for Claude 3.5 together: If I have a box filled with randomly oriented playing cards and I shake it until all the cards are perfectly stacked by suit (hearts, diamonds, etc.), entropy has increased according to the second law of thermodynamics, even though the system appears more ordered. Can you explain why this happens, considering the concept of microstates and how they relate to entropy in this scenario? ANSWER: This is an excellent question that touches on some key concepts in thermodynamics and statistical mechanics. Let's break this down step-by-step to understand why entropy increases in this scenario, despite the apparent increase in order.
Entropy and microstates:
Entropy is a measure of the number of possible microscopic configurations (microstates) that a system can have. The more microstates available to a system, the higher its entropy. This is expressed mathematically by Boltzmann's equation: S = k * ln(W), where S is entropy, k is Boltzmann's constant, and W is the number of microstates.
The initial state:
When the cards are randomly oriented in the box, there are many ways to arrange them. Each unique arrangement is a microstate. The number of microstates for this "disordered" state is extremely high.
The final state:
When the cards are perfectly stacked by suit, it might appear more ordered macroscopically. However, we need to consider the entire system, including the surrounding air molecules and the box itself.
Energy transfer:
Shaking the box inputs energy into the system. This energy is transferred to the cards, the box, and the surrounding air molecules. The air molecules gain kinetic energy and move faster.
Microstates of the entire system:
While the cards become more ordered, the air molecules become more disordered. The number of possible arrangements (microstates) for these energetic air molecules is vastly larger than the number of microstates for the slower-moving air molecules in the initial state.
Total entropy change:
The decrease in entropy from ordering the cards is more than offset by the increase in entropy of the surrounding air. The total number of microstates for the entire system (cards + box + air) has increased, leading to a net increase in entropy.
Irreversibility:
This process is irreversible. You cannot simply "unshake" the box to return the air molecules to their original state and the cards to their disordered state.
Local vs. global entropy:
This scenario illustrates the difference between local and global entropy. Locally (just looking at the cards), entropy appears to decrease. Globally (considering the entire system), entropy increases.
In conclusion, while the cards become more ordered, the energy input to the system causes a greater increase in disorder among the air molecules. The apparent contradiction between the ordered cards and increased entropy is resolved when we consider the entire system and understand entropy in terms of the total number of available microstates.
This example highlights the importance of considering the entire system in thermodynamics and demonstrates how local decreases in entropy can occur within a system, even as the total entropy of the closed system increases, in accordance with the Second Law of Thermodynamics.
You are the first person to actually explain entropy simply.
and wrongly.
Yeah, it's simple and wrong, so...
Explain your case.
If the organised dice are basically identical it doesn't matter which position they take, it's essentially the same state, so low entropy.
If they are disorganised it does matter which position they occupy resulting in more states = more entropy.
It shows because you needed to put in energy by shaking/twisting to organise them.
Well, this was absolutely fascinating.
Except there are not more possible configurations that the dice could occupy due to gravity. The dice can not float to those higher positions unless given energy by picking them up. Once packed they will stay packed in that configuration until acted on by an external force. I guess this is feasible in zero gravity but I’m not confident that would be the case.
really cool video, and love how you just casually throw in chat GPT in like "if I ask it the answer WILL be wrong", 10/10 chefs kiss
ok but is the rotation required to get this effect truly an entropic force? I kinda doubt it.
like, in order to get this effect you have to have the energy to produce a device that will produce this result, no?
because the systems volume stayed the same within the blocked u placed at 2:45, wouldnt the number of possible places for the die to be identical in both orientations? it seems like you just rearranged the dice while maintaining that the system's volume was equal in both cases (bounded by the stopper you inserted)
Also, since the volume of space occupied by the dice in the new position was smaller wouldn't that also counter the point you are trying to make?
Great topic! I always learn something, realize how little I know about something and not understand something altogether in every episode, it’s awesome. Keep up the great work!
This is wrong. Entropy is the degree of unpredictability of a system. With the mixed up dice, you have two degrees of freedom - each die can be anywhere, and also can face any direction. With the neatly stacked dice you only have one degree of freedom: Every die can be anywhere as long as it fits into the predifined grid. The first has infinite posibilities, the second has afinite (elbeit very large) number of posibilities.
entropy is defined differently in different fields. your definition of it sounds like it would be useful in information theory, but i think he's using the definition used in thermodynamics. the entropy of an isolated system always increases as a result of irreversible processes, and i think this counts as an isolated system and an irreversible process.
I run a Precious Plastic recycling workspace, here in Italy, in my spare time.
Usually I wash the plastic I collect in my washing machine (the european kind of, horizontal shaft), in a pillowcase, when doing laundry.
Often I have some boxes with sliding covers, the ones that contain carbide lathe inserts, or telescopic boxes for drills, and so on.
Sometimes I also have to wash bottle caps with child safety bottle caps (something from vaping fluids from friends and colleagues), made in two parts.
I break the external part to separate them, and then put them in the pillowcase.
Practically every time all of the parts come out from the washing machine re-assembled.
It's amazing.
The best explanation of entropy on the internet
This is why I love Thermodynamics. This is not only about "X" particles or things moving and doing things, it's something more fundamental.
I have a feeling that if you balance on stilts, you have a single wave destructive interference counterfore to keep balanced. If your stilts have 1 pivotal joint, you need a second order countermovement to balance. A rubber band is like a stilt with billions of joints which will always angle to eachother in some degree. Even when you pull the band until break, there will still be some amplitude of angular movement. When the rubber band brakes and would shrink at lightspeed, the shape it had just before braking will be amplified. Like a roadtrain with 10 lorries waving around hitting a wall. If something is bent in the sligtest way, it will bend that way during impact. For rigid object like a broomsting it's a batlle beween compression stress and shear due to material ununiformity(weakest link).
In thermodynamics, we were taught that entropy is the amount of energy that is not available to do useful work. As such then, something that is not available cannot create a force. External work was done on the dice and nails to get them into the ordered pattern. They did not get that way by themselves.
Interesting fact is that with the most symmetric geometrical shape, the sphere, you cannot get entropy by shaking. This is because there are two ways of 'closest sphere packing' (cubic and hexagonal). Both packing structures will occur when you pile up balls/spheres and shake them. They will form random groups within the pile of spheres, and the bounderies between those groups will only get more defined the more you shake.
I think this one's a little off the mark. Gibbs Free Energy is worth looking up
I recall reading that this is why cables in a box tend to get tangled with each other (or headphones in your pocket).
I gave ChatGPT your original question and it generated a similar answer to the one that you got, I then copied the transcript from this video give that as a prompt along with the instructions to read this and revise it answer, and it gave me the following:
Based on the provided transcript from the video, the concept of entropy is clarified in a more nuanced way. Here’s a revised understanding:
### Revised Answer:
Contrary to the intuitive notion that entropy is synonymous with disorder, the jar with the neatly stacked dice actually has **more** entropy compared to the jar with randomly oriented dice. This is due to the phenomenon of **directional entropic forces**.
### Explanation:
1. **Orientation vs. Translational Entropy**:
- **Orientation**: When dice are randomly oriented, their orientation entropy is high. However, when they are neatly stacked, their orientation entropy decreases.
- **Translational**: When dice are neatly stacked, they occupy less space, creating more free volume. This increase in free volume allows each die to have more positions it can potentially move to, increasing the translational entropy.
2. **Overall Entropy**:
- While the orientation entropy decreases in the neatly stacked arrangement, this is offset by a significant increase in translational entropy. The increased free volume provides more possible states for the system, leading to an overall increase in entropy.
3. **Illustration with Dice**:
- In a jar of randomly oriented dice, the dice take up more space and have less free volume, resulting in fewer possible states.
- When the dice are neatly stacked, the packing is more efficient, and the increased free volume means more possible configurations for the dice, increasing the overall entropy.
### Conclusion:
The entropy of a system is defined by the number of possible states it can be in. Neatly stacked dice create more free volume, increasing the number of possible translational states. Thus, the jar with neatly stacked dice has more entropy than the jar with randomly oriented dice. This reflects how entropy isn't merely about disorder but about the number of possible configurations or states of a system.
I always looked at entropy as the ending of something or decay but there's more to it. The heat death of the universe was the main example of entropy i had used to try to figure out what entropy is/does. Even in this video towards the beginning it seemed to me more like the tendency to even out, before you explained it more.
So what I get from this is entropy is the tendency to or force of changing to a state of more potential from a state with less potential.
This video reminds me of my younger days back in the 90s. I used to prepare for raves by visiting a stimulating trader I knew.
I was still young and naive and didn't understand why this friend would always take out a large bowl filled with dice and marbles. He explained that sometimes its not enough to hide the screwdriver.
As my experience grew and I met different people I understood, Dude was just protecting his electronics with that bowl.
3:42 bro, what website is this?
I'm skeptical that this video is correct. At 2:39, the amount of free volume per die has not changed at all; it is simply a different arrangement. There are, in fact, fewer possible states with the dice packed orderly than randomly. The dice stacked like that is the same as all of the air in a room being in just one half of it: it wouldn't be a stable state if there wasn't something else going on. What you have accomplished is more equivalent to a phase change, from an amorphous solid to a crystalline solid. The phase change is brought about by the loss of gravitational potential energy (as sound and heat) as the dice settle into lower positions. Yes, entropy of the system has increased, but no, entropy of the stacked dice themselves is not greater.
This should be testable by performing the same experiment in a zero-g environment. I, unfortunately, lack the resources to go to space to perform the test. Any ISS astronauts here who want to play with dice?
You can still call entropy disorder, but just be careful of what you define as your system. For example, the dice ordering and leaving the volume has higher entropy, but if you were to consider the system as only the dices, and therefore don't consider that bit of volume that "creates" later, the entropy is lower.
On a microscopic level it's easy to call entropy disorder, but on a macroscopic level defining systems is hard
The example of the elastic band and the curled string of particles was really cool!
Please, someone correct me if Im wrong, but I understand that the order inside the Jar its only acquired after increasing entropy, because putting the dices inside the jar (a glass crafted with specific shape, proper to contain things in a certain way) it is already a anti-entropic movment... the entropy inside the jar its only coming to an aspect of order, because we are considering a closed system, ignoring that the jar was crafted in a certain shape (and also the dices), and separating therefore that closed environment from the total chaos of the universe.
Would that work with thermacol beans ? I think not to the extent since the weight is negligible in beans than dice and nails.
This is more about the phase transition, not simply by entropy which should consider the free energy. Entropy is a part of free energy and phase transitioning to a more ordered system cannot be solely described by entropy. During the process, the entropy of the dice decreases by gravitational force and friction. Entropy is simply a number of possible states a system can have.
if only science class was this interesting
I won’t claim to be any expert, but I think the claim is that nature tends toward less organization. But an obvious exception is when an organizing force or energy is added to the system. For example you can separate ions using electricity or separate metals using magnetism, or separate different densities by gravity. In the case of the dice you have gravity and the shaking both acting toward the dice entering the lowest potential energy state, which happens to be more compact and ordered.
If you shook the dice without any gravity, it would likely remain jumbled.
I was under the impression not that entropy was related to the total number of states, but the percentage of total states that contain an equivalent amount of information. There are a higher number of states where the dice are arranged essentially randomly than when they are packed. You also have more information density as to describe the position of the dice, you basically only need the diameter of the largest ring, the number of rings, the width of one doe, and the height of the stack. For the randomly oriented set, there's no way to predict the position and rotation of each die other than nothing down all quantities for all dice. Both of these would suggest the opposite entropic relationship (if my previous understanding of entropy was accurate... Which is not something I'm confident in)
This video gives me a new view of force, force is a difference of possibility, interesting
2:30 is an interesting explanation, but I was just going with "gravitational potential energy" instead. As a thought experiment - if you were to repeat this experiment in a non-accelerating frame-of-reference, say on the ISS, would the dice self-organize too?
I love how your simple questions and demonstrations arouse the curiosity of so many. I never considered the entropy of a cup of dice before, for example.