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There has been quite a lot of fuss over the years to explain why the Demon does not represent a violation of the Second Law of thermodynamics. Many papers bring information or complexity theory on board, explaining either that the recording or the discarding of information supplies the missing entropy, or else re-defining a new entropy which will in increase despite the Demon's efforts.

Why do all these authors have such a strong expectation that some argument must be found to restore the second law? Given what I think is a standard understanding of entropy, there is simply no reason to expect this.

Once an agent's preferred macro-parameters are settled, phase space is divided into chunks and entropy refers to the volumes of these chunks. A different agent, with access to a differing level of experimental control, would have a differing set of macro-variables and a different partitioning of phase space. Such an agent could definitely implement what appears to be, on the first agent's partition, a decrease in entropy. Couldn't they?

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    $\begingroup$ This has bothered me forever. I hope it gets a good answer. $\endgroup$ – WillO Nov 29 '19 at 21:15
  • $\begingroup$ Any physical demon that has been thought or experimentally tried does not work, see those two sections here, en.wikipedia.org/wiki/… $\endgroup$ – Wolphram jonny Nov 29 '19 at 21:20
  • $\begingroup$ Even if the Landauer Limit has been experimentally verifies, as the wiki article claims, the Demon can still decrease entropy to an arbitrary degree for arbitrarily long periods by having a sufficiently large memory. It just can’t keep it up in the long (possible long long) run. $\endgroup$ – DPatt Nov 29 '19 at 21:24
  • $\begingroup$ I am voting to close because, without any fundamentally agreed upon conclusion, the question of the validity of Maxwell's Demon remains, to date, primarily opinion based. $\endgroup$ – Bob D Nov 29 '19 at 23:10
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    $\begingroup$ Isn't the onus on someone to prove that a case with decreasing entropy from a Maxwell's demon physically could exist, with acceptable approximations? Not the other way around, for people to prove something couldn't happen that they have no proof of it in the first place. It's a thought experiment but has a proof been given? $\endgroup$ – user234190 Nov 30 '19 at 0:59
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The standard version of Maxwell's Demon allows for a perpetual motion machine, producing an infinite amount of work from a finite-temperature reservoir. This seems too good to be true, and since nobody has ever successfully built a perpetual motion machine, it is widely believed that these are unlikely to exist.

A number of physicists believe that Maxwell's Demon has been exorcised. This was done using Landauer's principle:

the minimum possible amount of energy required to erase one bit of information is kT ln 2.

In order to operate, the Demon needs to remember which way he sent the molecules. Eventually, his memory becomes full, and he is unable to keep operating. Once he starts erasing his memory, he can no longer reduce the entropy of the system for free.

Viewed in another way, the Demon is simply a heat engine that operates on the difference of temperature between the system and his memory (which has temperature 0).

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  • $\begingroup$ This is a brilliant answer. The best thing about Maxwell's Demon is the way that it demonstrates that "thermodynamic" entropy and "information" entropy are the same thing. $\endgroup$ – user68014 Nov 30 '19 at 16:48
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    $\begingroup$ Thanks for the answer. What is the status of Landauer's Principle? The two possibilities are 1) It is justified because of its relation to the Second Law, which is justified by other means, and 2) It salvages the Second Law, and it is itself justified by other means. Not that I have a problem with the logic of 1, though I think 2 is preferable. $\endgroup$ – DPatt Nov 30 '19 at 19:08
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    $\begingroup$ @DPatt: I believe Landauer discovered it through thinking about reversible computation, and only after he discovered it did Charlie Bennett realize that it salvaged the second law from Maxwell's Demon. His original paper doesn't mention Maxwell's Demon at all. I don't know what the status of it is if you're looking for a rigorous mathematical proof of it, though—physicists don't generally care about these. $\endgroup$ – Peter Shor Nov 30 '19 at 19:11
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If a physical process could bring about an energy movement from a colder to a hotter body, with no other change, at the macroscopic thermodynamic level, in the rest of the universe (this what Maxwell's thought-experiment purports to do) then it would mean the 2nd law did not hold universally (in the thermodynamic limit where it becomes a precise statement). However, no one has ever succeeded in proposing a physical process which actually achieves this, so as far as we know the Maxwell daemon is a physical impossibility.

It is good practice to invest intellectual effort in this way, I mean to check that a process ruled out by the 2nd law is indeed not possible, because it helps our understanding to know that the 2nd law does indeed hold. This is important because that law, or descriptive principle, plays such a useful role in many areas of science, especially chemistry.

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  • $\begingroup$ I may not be up-to-date on my Applied Demonology, but aren't most proposals "mindless" in a sense? The spring-loaded flapdoor and the ratchet based systems are, I think. What I mean is that they operate the same way no matter the gas configuration, whereas an intelligent demon can choose amongst operations upon learning the gas configuration. How many proposals like this are there out in the wild? $\endgroup$ – DPatt Nov 30 '19 at 19:25
  • $\begingroup$ Actually Szilard's Engine is intelligent in this sense, I think. $\endgroup$ – DPatt Nov 30 '19 at 19:26
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Why do all these authors have such a strong expectation that some argument must be found to restore the second law?

Could it simply be because no one has ever actually observed violations of the second law? Just like no one has ever actually observed speeds exceeding the speed of light?

Hope this helps.

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    $\begingroup$ This would be due to nobody actually constructing a demon. $\endgroup$ – DPatt Nov 29 '19 at 20:25
  • $\begingroup$ @DPatt I think that would be a good way of putting it. $\endgroup$ – Bob D Nov 29 '19 at 20:26
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    $\begingroup$ @DPatt: I don't believe that this was for lack of trying. Maxwell's Demons are either impossible or incredibly difficult to build. Doesn't either of these possibilities need an explanation? $\endgroup$ – Peter Shor Nov 30 '19 at 15:05
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Obvious violation of the second law of thermodynamics:

Deionized water in an electric field:

https://youtube.com/watch?time_continue=7&v=17UD1goTFhQ

The turbulent motion is powered by ambient heat (no other source of energy is available) and can convert this heat into work, e.g. by rotating a waterwheel.

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    $\begingroup$ I downvoted. Energy from heat can provide work, in a smaller amount. This goes on in the machines called heat engines. So merely to say that one has a machine powered by heat is not enough to claim that the 2nd law is violated. When one analyses such machines, the entropy overall stays constant or increases. A heat engine typically works by moving entropy from a hotter to a colder region. $\endgroup$ – Andrew Steane Nov 30 '19 at 14:23
  • $\begingroup$ Converting ambient heat into work doesn't violate the second law... If that were the case, we would already have proof of Maxwell's demon from the drinking bird. We know that it doesn't violate thermodynamics though. $\endgroup$ – JMac Dec 2 '19 at 14:45

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