Maxwell's Demon - Why Information is Entropy
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- เผยแพร่เมื่อ 24 มี.ค. 2018
- James Clerk Maxwell’s idea for violating the Second Law of Thermodynamics. Video also covers reconciling the information theory of entropy with the macro-state / micro-state definition of entropy. My Patreon page is at / eugenek
- วิทยาศาสตร์และเทคโนโลยี
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я в восторге от вашего демона, вы можете прислать её 3д модель. я хочу сделать такой же потрясающий костюм
So in other words if you know more you can think of more thus increasing the Entropy of your Brain?
And in also other words if we forget something it will be radiated away by elecromagnetic Wave? Is this correct?
I like how the demon is doing yoga in their spare time between opening the door
Also she's Chinese and has bat wings
@@-ahvilable-6654 thats racist but whatever it will still
It was not her spare time. It was the time to erase information (memory) by generating heat and increasing the overall entropy.
It is nice that she does yoga to erase her memory, though.
😂😂😂👏🏼 comment of the decade
@@FelipeSJardim I have a question, can you explain me that why erasing memory will result in dissipation of heat in the surroundings?
The reason I *like* these videos is that they’re informative. The reason I *love* them is that they’re just kinda surreal. Keep it up.
Thanks. More videos are on the way.
@@EugeneKhutoryansky This explanation bleeds from many wounds. 1.) WHY is needed an entity (Demon) with memory and keep track of the location and velocities of the molecules, why cannot use an automatic system which just measures the velocity of the incoming molecule, and if it is a "high speed" molecule let it through, thus no need to memorize anything in the first place, and 2.) WHY just those bit operations means dissipation of heat - release of energy - which means an erasure of data, why not any operation? What distinguishes delete operation from write operation, bot of them are just settings of states. So I can create energy?
Gergo, this is explained in detail at arxiv.org/pdf/0707.3400.pdf
@@EugeneKhutoryansky THANK YOU SO MUCH. WHICH COUNTRY ARE YOU FROM?
@@gergo01Physics works the same for a human and a machine, both acquire information and store it. Your knowledge on the subject bleeds from many wounds...
I never knew that Maxwell's Demon was so cute.
0:10 "it's not her fault that she was born looking this way"
Indeed
This reads as some whack slice of life anime title
My Little Maxwell's Demon Can't Be This Cute
"My imouto keeps violating -
- the Second law of Thermodynamics"
Why does she have light coming out of her nostrils?
When physics and demonology needlessly overlap
Physics and demonology are a match made in hell and I live for it
@@williammanning2938 please explain how measuring and understanding the physical universe has anything to do with demonology.
How much does a demon weigh? How fast can they accelerate?
What is their top speed?
@@unitedspacepirates9075 no
Needless per say. Per say.
@@unitedspacepirates9075Demons are quantum entities subject to Heisenberg's uncertainty principles. Your questions essentially lack meaning, do you know how much tornados weigh ?
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Physics Videos by Eugene Khutoryansky sir can u send me your WhatsApp number ....
Why should erasing memory cause dissipation of heat into the surroundings?
Please do some videos about electricity and power and power multipliers transistors . I am a big fan of you . Keep up the good work
Joe Crowley, actually you do not necessarily have to dissipate heat to assign a value to a register with nothing previously stored in it. It is clearing the register that will dissipate heat, unless the value of the register is transferred to another location such that no information is lost.
199sec, thanks. I am glad you like my videos. I already have a very large number of videos on electricity and several videos on transistors.
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Yes, my email is eugene381@comcast.net
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Is the "entropy of the mind" related to the collapse of a quantum waveform? And is that related to the way statistics are easier to estimate than individual outcomes? That second one is explained with simple math, but it feels like there's a "there" there. I know you've touched on all of these topics individually before.
Yes
@@ishworshrestha3559 interesting. Thank you.
I am going to have my wife dress up as Maxwell's Demoness. That filigree outfit will look hot on her. It will all be in the name of science.
You should probably ask her first. Otherwise, best be safe and buy the costume in your size... good luck with that!
in the name of research
Lmao
Ok but there is no sex allowed. Only opening doors for atoms. She need to stay in her role.
The problem with our world is, those who do shitty and useless jobs get more subscribers whereas people like Eugene Khutoryansky who does an impeccable job in teaching science are not appreciated well enough by the public. I wish, sir, your channel grows exponentially.
Thanks.
We would do well in this country if this channel were required viewing!
I think she's a Miss and not a sir
Ohh is that so?
#justneckbeardthings
Thank you for all your hard work in consistently making such quality videos; you are a notable example of industriousness for the public good
Thanks.
The videos are basically essays with CGI illustration. Thank you so much for these.
Glad you like my videos. Thanks.
i was watching your video on quantum tunneling when i got notified for this one! love your passion for physics!
Thanks. I am glad you like my videos.
Sir your videos are extraordinary and provides in-depth visualisations and explanations for core topics in science, even though today's world is highly developed, technological and digitalised it's hard to find videos comparable to yours. I really appreciate your efforts in clearly understanding the concepts and presenting them accurately through powerful animations
Thanks for the compliments about my videos. I am glad that you like them.
This is a very good method of teaching. It literally involves my thinking to the level of being mentally immersed in the concept. It"s truly amazing!
Thanks for the compliment.
One of the very few informative vids on youtube that I actually got hooked on to. The details are so subtle yet mesmerizing. Grande tutto benne
Thanks.
You are the best -- no other presenter can do it better.
You have special skills to explain the most complex Physics topic in such a visual way that every one understands! It makes sense immediately!
Thanks for the compliment.
understanding the universe is like a religious experience to me < 3 thank you so much for these
Glad you like my videos. Thanks.
Ironic that science is as close to God as we get.
_•hits blunt•_ Yo, what if Global Warming is caused by people experiencing too much and then releasing their memories as heat when they die?
yo wtf thats a legit thesis worthy lmao
Fascinating! Would love to watch and listen more about the Second Law! Thanks a lot Eugene.
Every one of your videos is amazing because it links the mathematical concepts so well with visual representations. I wish I had known of your videos when I was in school!
Thanks for the compliment about my explanations.
"It is not when we acquire information that we pay a price, but when we attempt to forget it."
This is why it's so hard for me to get over my ex...
I think this statement is not quite correct. Acquiring information increases entropy too. For example, say we want to save some information in digital format. For that, we'll need to specify one exact state of each bit out of two possible states (0 or 1). This can only be done by expending energy (say a certain voltage difference across a logic gate). So storing information too increases entropy.
*This explains why getting her/him was so much difficult as well, LOL.
Anik Samiur Rahman
That is not correct. Entropy does not increase whenever something uses energy. The energy to flip the logic gate could come from the system itself. It is only when the *usefullness* of the energy decreases that entropy increases. For example, when energy changes from coherent to decoherent, or from high frequency to low.
In my view this is the best physics channel on youtube. Thank you for providing us with these awesome videos. The explanations are always on point, the short pauses are perfect for thinking on one´s own parallel to the video and I love the background music. It really helps to focus on the explanations. Thank you for this great content.
Thanks for the compliment about my videos.
Already looking forward to the next video, they are always great!
Thanks. I am glad you like my videos.
I learn so much from your videos, and the animations are Amazing!
I never thought physics can be visualized in this astonishing way! thank you!
and can you please add references in the description comments section!
this is his reference : Nature volume 483, pages 187-189 (08 March 2012). yeah Eugene have some artsy sides
Great video as always
Thanks. Glad you liked it.
love your stuff, high quality and good for those who are not physics buff
Thanks.
One of the best channels I've ever follow. Keep up 😉
Thanks for the compliment.
This is awesome, I had never thought of information as entropy. I recently heard a quote that progress works against entropy, but what if progress is the material manifestation of negative entropy caused by the positive entropy of information.
@@amberstiefel9748 it makes my brain hurt! maybe if they first explained why this is important? or at the end?
Photons have energy so informations will always be entropy
Huh, in information theory information is literally defined by entropy.
This is actually such an impressive video as a nascent content creator. The animations, demonstrations of concepts, demon, really fascinating. I want to learn how to animate 3D objects like this.
your way of explanation is amazing, also the animations
Thanks for the compliment.
Excellent video Eugene! I have always had problems with this topic. Than you for explaining!
Glad you liked my video. Thanks.
Fabulous, love to watch your videos
Glad to hear that you like my videos. Thanks.
Really u made physics interesting for me , thanks a lot now I have found out a new way to learn and understand things😊😊
Thanks.
I love your videos, please don't stop making them.
Thanks. More videos are on their way.
was just reading about it from blundell ... and this is the first video i got after searching on youtube. as usual fantastic
Maxwell is also famous for his silver hammer.
Bang, bang!
And coffee
Yeah yeah, and magnetic tape, too.
*No, that's Edison you must be thinking of...*
Maxwell Edison was majoring in Medicine
_before_ the incident with his silver hammer.
silver hammer win
Great animations... Thank you for your effort
Thanks. I am glad you liked my animations.
Naw, they're always creepy
"EXCELLENT"..... beautiful presentation... described in simple and plain language...it helped me to understand entrpy/ information.. request to to keep making such videos in all such difficult subjects .... thanks 🙏.
Thanks for the compliment. More videos are on their way.
Very clear and easy to understand, as always. Thank you!
Thanks for the compliment.
Could you make a video on why deleting information dissipates energy?
I luv this channel...
Thanks. Glad to hear that.
I love your videos. Please keep them coming.
Thanks. More videos are on their way.
Physics Videos by Eugene Khutoryansky how about one on quantum field theory and identical particles.
That's on my list of future topics. Thanks.
one of the GOATs of youtube channels
Did I miss where she says "why" information is entropy, and not just "that" it is?
No. No, you did not. I also noticed that. I also noticed that the reason why forgetting information would produce heat wasn't explained either.
Let me try to give my own explanation:
Information is that what distinguishes 'something'. If you have a bit that can be either a 1, or a 0 then that's a way to distinguish those states. Reading off that bit as 1 distinguishes that bit from 0. That's why you can count information in bits, since a binary distinguishing is the most simple.
Entropy is the number of "ways" 'something' can be. So a classical bit can be in two "ways" (states), namely 0 or 1. So the entropy would be 2. (For other reasons, entropy is actually the log of the number of states, so log(2) in this case.)
This doesn't sound the same so far, but now consider if the 'something' we're talking about is in one of its states (so again, either 0, or 1), but RANDOMLY so. That is what was meant when in the video he said to assume all micro-states were equally likely. If all micro-states are equally likely, the macro state will be one of the ways of arranging the microstates, at random! If you now want to distinguish this macro state from another macro state, you would have no choice to use as many distinguishers (Bits, 0's, or 1's) as there are microstates, since the microstates are at random. So then the information (The distinguishing thing) and the entropy (the number of ways it can be) are the same.
Therefore, the key is to look at random information. Let's do an example to show you what I mean.
Say I have a (non-random) message containing the information: 100100100100100... etc. If I want to send this information to someone, I could compress the message (and thus the information.) by making use of the predictable (non-random) regularity of the message. I could for instance just write 100... repeating. I would only need 3 bits to do so, instead of the many bits in the original message. This is called information compression, and is used in computing and communications all the time.
Now, were I to have a RANDOM message like; 1001101011001000101... (Excuse my inabillity to be truly random), without any regularities, I would have no choice but to send the full message, so all its bits. In the case of random information, the number of ways and the information itself are the same. Hence, the information and the entropy are the same.
It is a quiet assumption that in quantum mechanics all possible micro-states are equally likely. So then we're always talking about random information, and information and entropy are always the same. You could also argue that in the case I have information with a pattern, like the 100... example, the extra bits I use for the repeating information is redundant, and not reflective of the "true" information in that message. This "true" information of something is what phsyicists talk about when they say information. It's also been called Shannon-information (After Claude Shannon, father of information theory) or Shannon-entropy. As this will always be the same as the entropy.
I hope this helps somewhat. You can continue this reasoning for the reason why 'forgetting' increases heat, but I feel like I already wrote too much. If you want to look it up, it's called Landauer's principle.
I was hoping the video would explain this. And not exactly these words, but using his own understanding of the concept. It helps me to hear different angles on the same thing. You could also explain entropy and information using the concepts of equilibrium for instance.
So, if anyone that has read this overly long youtube comment wants to do me a favor, please write your own understanding of why information is entropy. Or maybe continue with the forgetting -> heat example. I will enjoy reading them :)
@@jojoviviator9258 I should think anyone would have a difficult time explaining the concept more succinctly! Thank you for the elaborate and well reasoned answer.
I hadn't thought of information as a that which distinguishes, but upon deliberation it is possibly the best definition. Hawking radiation takes on a whole new meaning for me now, and would I be wrong in seeing it as an example of loss of information causing heat increase?
I too would love to see people increase this thread. Just don't delete anything. My phone gets hot enough already 😋
Jojo Viviator quite helpful, thanks!
@@jojoviviator9258 hey. Even though I agree with what you said, it makes sense in a way. I'm still not really convinced that information is at the nature of the universe. Everything we can see is just change. Every measurement is basically a delta. Science is all about delta's. It's everywhere. Even so much that most don't even care to put it there. I simply don't think that these "true" and absolute informations exist. How do you think entropy would work if we just don't accept that there is an underlying truth to it. That the reality is just a derivative of time and by taking the integral we could determine the underlying truth. Or rather the underlying information. It's a bit of a weird way of argumenting, since the math works out, but I don't think that you could consider time to be space like how Noethers theorem suggests. There's no causality and no anisotropy in space. Why should we be able to take integrals of time and just expect it to work, where integrals are just a mathematical tool used for description of space. I say there is no information and everything that exists is change. I believe the second laws of thermodynamics to be true, so how do you think we can solve Maxwell's demon without relying on information as a thing that exists in reality?
Let me know if that makes sense or if it's just crazy me talking.
Jojo Viviator For the reason why "forgetting" produces heat:
Memory in both computers and brains is stored in the form of a voltage difference between a positive charge and a negative charge: in computers it is a capacitor, in a neuron it is an action potential. Erasing the memory means "sparking" this voltage through a conductor, therefore creating an electric current, therefore producing heat.
That pout! XD
A really excellent video as always.
Thanks for the compliment.
you are a great explainer... i found them truly helpful in understanding a number of concepts.
Thanks for the compliment and I am glad to hear that my videos are helpful.
If she forget the memory in vaccum where does the heat energy go to increase the the entropy of particles to offset forgotten information entropy(if her brain is hypothetical and not surrounded by any flesh to transfer heat).
Heat energy can always be converted into photons, and the photons will then travel out into the vacuum of space, carrying off this energy.
@@EugeneKhutoryansky But why exactly does she need to forget that information? She already did her job and can just stop with the door opening.
@@argoargishtin5187 thought it said if she runs out of space. She will forget .
would it not take longer and longer lengths of time to partition the gas molecules as difference in densities increased?
Yes, that is correct.
Your videos always amaze me
Thanks
Glad you like my videos. Thanks.
Your video has considerably increased my brain's entropy.
Does this mean that information is conserved or increasing in the universe?
Conserved
How could we forget something thinking about forgetting it?
I had experienced tiredness and hunger thinking too much but never by forgetting.
This is an advanced level of self mastery that you can achieve through rigid discipline of practice and meditation, ideally only requiring a few years but realistically requiring several cycles of births, deaths and rebirths, in an indefinite process which might still only result in a possible failure to fully actualize the power using fundamentally opposite forces of the mind to juxtapose them into symmetry of the unintuitive new system.. Wait, what? What was the question again? I'm trying to take a shit; leave me alone and go ask my soon to be ex GF since she is the Oracle of All Knowing Omniscience, Most High and I'm only a NaggerLord Cum-Master Excellent, obviously not in any position to expose upon such matters.. *bloop* -flush-
Amazing Video. Thank You. You never fail to blow my mind
Glad you liked my video. Thanks.
I like your entropy videos. Cheers
Thanks.
But what if we build a robot which randomly opens & close the door
And it just happens that particles get accumulated
As their is no memory,entropy decreases
That is the same as a scenario where the door is always open (same as a door not being present), and the particles just happen to all gather together on their own. The probability of this happening is so low that we would have to wait several orders of magnitude longer than the present age of the Universe to see it happen.
Sure, the chanses of that happening is extremly low, BUT its theoretically possible and the second law of thermodynamics (as i have understood it) is that the total entropy of a system will NEVER increase.
Does this mean that the second law of thermo dynamics is wrong? Or, more likely, does "never" (in the sentence "the total entropy in a system *never* increases") mean "practically never", so that you cant make a machine that reliably lowers the entropy in a system (like maxwells deamon)?
Mom's Spagetti, I deal with that topic in detail in my video at th-cam.com/video/vE82PDJB8ow/w-d-xo.html
@The physics talks: I have thought even more what about if the demon has a statistical model in him/her mind such he/she not open the door randomly but following a certain distribution probability he/she would not have to remember all the positions and hence not memory problem will arise.
Please take into account the Landauer's principle.
I have thought even more what about if the demon has a statistical model in her/him mind such he/she not open the door randomly but following a certain distribution probability he/she would not have to remember all the positioins and hence not memory problem will arise. Please take into account the Landauer's principle.
I wasn't knowing, memory is a form of energy.
Amazing.. as always. Thank you for your videos
Thanks. I am glad you like my videos.
Great tutorial! Amazing illustrations! a solid 10!
Thanks.
The music is giving me Madoka Magica flashbacks
hahhaha. Weeb.
@@dragonsmith9462
i love madoka magica with a passion
Maxwell's Demon seems like a nice lady. I'd like to hug her.
how about boning
much love from Morocco keep it up eugene
Thanks.
amazing video as always
Thanks.
maxwell's demon is a total qt3.14
qt3.14 mean quantum tunelling march 2014
true qt3.14
Cutie pie
please stop trying to seduce my thought experiments, Fate already turned most of my favorite historical figures into anime girls can't we just leave this be
Yep and now this is what Musk has called his kid
7:17 shows how demon can hear everything in universe.
Damn! That explains how those 'entities' can perceive things we humans can not.
Thanks it was too simple and awesome to explain the stuff
i love this videos, makes me feel very inteligent after watching, even though i understood little
Thanks. If you had trouble understanding this video, you may want to start out with my introductory video on Thermodynamics at th-cam.com/video/GOrWy_yNBvY/w-d-xo.html
in before thousands of views, fame and glory!
Eh we've been thinking that for ages, mate :D
Music makes awesome
this is the art of science.
Excellent Video, breaking down and debunking Maxwell's Demon. Thank you Eugine.
Thanks.
The calm rationalism in Eugenes' presentations is superb.
Thanks for the compliment.
You deserve it.
Have another - Eugenes' patient replies, to questions and views expressed in the comments, are professional and very pleasing to see.
by watching this video my entropy of information also increases
So she generates heat to forget but dont generates heat to create the memory in the first place?
Very interesting! I was curious about the meaning of information in physics. It is because I learned wave conveys energy and information and wondered why information. This video could solve my curiosity a little bit! 🤍🤍🤍
Thx for making such a useful video
Thanks.
so this confirms that information is actually physical
depends on what you define as physical, I suppose
@@Robert_Gray somthing subject to the laws of our universe.
@@julioequinones whos youniverse?
But we have to avoid stating things as plainly as that. Because if people know that information is physical, then they'll speculate that conscious agency contradicts 19th century materialism and its Marxist implications. That invariably leads to wooh wooh new age fantasies, which in turn inspire science fiction writers who then go on to write stories that contain impossibilities, that later become commonplace reality.
I'm just trolling.
How can deleting information form brain dissipate heat? Is there a biological reason?
Also I heard about this Maxwell's demon in one of the documentary, it is really interesting. We make and break things, just by doing that we increase the entropy of the universe. Is it good if 2nd law of thermodynamics was violated?
I don't know if the heat dissipation is true. You can't just erase information. If you do so, your actions will change your surroundings, which will leave a trace of the information. It's just transfered, like energy.
Prathamesh, it does not have to be a biological brain. The same phenomena would happen if we tried to erase information from an electronic computer. And yes, it would be a good thing if we could violate the second law of thermodynamics, because then we could have unlimited usable energy, and all life in the Universe would not necessarily have to come to an end when all the stars in the Universe deplete their nuclear fuel.
Physics Videos by Eugene Khutoryansky Its too bad you couldn't edit the video to say that and maybe add a short explanation for why erasing info from an electronic brain would create entropy. I bet lots of people are confused about that.
Thanks for the videos.
peoplezk1, I mentioned at the beginning of the video that is also true for electronic logic gates, so I think that part is already covered. What is missing is showing "why" this is true, but that would require a video at least as long as this one, if not much longer.
Well I was about to ask this myself. I am definitely interested in why this is true.
Thank you! I've never seen a more clear example!
Thanks.
Great animation thank you for your efforts.
Thanks for the compliment.
I come to know what entrophy meant. Ok i just googled, it's state of confusion, disorder and disorganization. Back to the video. 💕
Actually, entropy is not disorder. That is a common misconception. I cover this in my video at th-cam.com/video/vX_WLrcgikc/w-d-xo.html
You may want to start with this video, though: th-cam.com/video/GOrWy_yNBvY/w-d-xo.html
No matter how hard the wind blows on a beach or in which direction it blows, the wind will never build a sand castle. It will only move the sand around to different positions.
Robert Calk Jr. according to the law of probability you are wrong
According to entropy I am right.
nVidia - The way its meant to be played.
Another great video!
Thanks. Glad you liked it.
How about the demon opens the door randomly and it happens to be always at the right moment cause of probability and therefore decreases the entropy of the particles and no entropy increases by opening the door randomly?
No
@@themass2517 No?
I think I'm in love and it's driving me crazy! But at least I know what state I'm in.
If information is entropy, does this mean that the total information in the universe is increasing?Where is the new information coming from?
Sarvani V if you think about it in the macro-state way explained in the video, you could imagine the first moment of the universe as a singularity with only 1 macro state. Since the universe is increasing in entropy, there is a direct correlation between entropy and information
Thankyou everyone.
Murat Yüksel , I think the same too. But it turns out that the information of that instant of a quantum particle doesn't affect the outcome. They are literally RANDOM. Also we can't get much information from a superposition...
Correct me if I'm wrong. 😊
I think even this:
While a particle is in superposition, it has very little information. But if we measure it, it collapses to an outcome. Therefore if this event was random, new information has been created.
Correct me if I'm wrong.
The Black Cube of Saturn
Whoever figured out the information theory explanation for Maxwell's Demon not violating the second law is a freaking genius. I could think about this for a lifetime and never make the connection between entropy and information in the Demon's brain. And then to close the final loophole regarding heat and erasing information. It's just beautiful and brilliant.
It's more intuitive than you think. All forms of information require physical interaction, that's the whole basis behind quantum superposition. By measuring it you change the outcome. You can't know something without affecting something. There is no such thing as a perfect observer... except maybe God.
6 years of studying Mechanical Engineering and a few TH-cam videos explain entropy better than your typical thermodynamic equations.
and with a hot succubus
This makes no sense at all. The door opening and closing is frictionless, but the imaginary demon forgetting bits creates heat.
Having zero friction does not violate the known laws of physics. On the other hand, erasing information without increasing the entropy of the surrounding environment does violate the known laws of physics.
How?
Please demonstrate a demon that can open and close a door without releasing more heat than the act of her thinking. That is beyond ridiculous.
Several implementations of this basic concept have already been done using quantum physics. A detailed discussion of the physics of Maxwell's Demon is available at arxiv.org/pdf/0707.3400.pdf
Say I take for granted that this situation makes sense. How did you determine that the entropy gained by forgetting a bit is greater than the entropy lost by the act of opening and closing the friction-less window? This theory sounds like one of those ad-hoc, imaginary, hole-plugging theories, an example of which would be Hawking's "black hole evaporation through quantum fluctuation" theory. In other words, this heat released by a forgetful demon stuff is just an attempt to support the widely held scientific belief that there is no way for the entropy of a system to decrease, even temporarily.
I like your videos. Like really! Humbling
Thanks.
information means what ? why entrophy changes ? what about things that dont exists but lets say i think ? what if i go outside of the universe ? is this only about only statenents or what ? thanks for giving questions instead of answers :)
The animations of these are amazing
Thanks for the compliment about my animations.
Your videos increasing entropy in my brain.
this video made my room slightly warmer.
Thanks for the video!
You are welcome and thanks.
That's really, really interesting!
Glad to hear that.
Great video. Love the animation and overall presentation. Though I don't follow why entropy should increase just from watching the particles. It seems only the memory clearing part necessarily increases entropy because it can't be done reversibly.
Thanks. The issue is what would happen if the demon had a sufficiently large memory and never had to erase any of her memory during the entire experiment. The demon is unable to decrease entropy of the universe by forcing the particles into one specific state, because in order do so, she has to remember the previous location of the particles, and her memory can therefore now be in a number of different configurations, from our perspective. When something can be in a larger number of configurations, this means that its entropy has increased.
Your videoes are just awesome... All of my friends has begun to subscribe your TH-cam channel...#GREAT VIDEOS
Thanks for the compliment and I am glad to hear that all your friends are subscribing to my channel.
What is the name of the music at the beginning and at the end?
Hey Eugene,
Awesome videos! How do you know so much about these topics? do you have a degree in physics, do you do a lot of research or both? And do you have any good resources where I could learn more about these topics like textbooks or websites. Thanks again for the great videos!