Has maxwells demon really been proved impossible

Factual Questions
1

As I understand it unlike the first law of thermodynamics (you can’t win the game) the second law of thermodynamics (you can’t break even) is more of a suggestion than an actual law, Entropy increases not because it must but because statistics and probability make it much much more likely to increase than decrease.

So on to Maxwell’s demon, a thought experiment that Maxwell figured might get around the second law of thermodynamics. In the end it was pointed out by others that running the demon would take energy which would increase entropy (you still can’t break even). But this doesn’t prove that an entropy reversing demon is impossible, just that the supposition of a demon doesn’t disprove the second law.

Now I’m not in any was shape or form arguing that the second law is indeed false, I’m just wondering whether the hypothetical science fiction construction of such a demon would require a massive rewriting of the laws of physics, or just the modification that entropy increases except when you use a demon.

2

If the demon uses energy, it increases entropy. Above and beyond the entropy being reduced by the expenditure of energy.

3

But how do we know this. Of course we all believe that the demon would increase entropy more than its actions would decrease it, because if it didn’t it would violate the second law, and we all believe the second law. But we believe the second law because we believe that there is no such thing as an entropy reducing demon. This seems a bit circular.

I guess what I am asking is suppose I had a entropy reducing Maxwells demon in my pocket. Would this be as eath shattering to science as my having a faster than light space ship, or would it just require an eception to that one law.

4

Yes. Plenty of people have tried to get around this in the past century, but it’s been proven even in its strictest possible forms. From New Scientist:

5

I’m not sure that the hypothesis of Maxwell’s Demon really adds much, because it’s essentially circular: if the 2nd Law holds, the Demon is impossible, because the Demon must obey the Law; if the 2nd Law does not hold, you don’t need a Demon.

I think the deeper issue that maybe you’re trying to get at is the nature of the 2nd Law. The question of whether it’s an empirical law that might be wrong (and if so what would that mean); or in what sense derives from other more fundamental properties of the universe.

6

Yeah I think this the heart of what I am interested in. When it comes to FTL travel, I believe its impossible because we can work out that accelerating to that speed would require infinite energy, and that doing so would violate causality, both of which are pretty hard to get around.

But with the regard to reducing entropy it seems that we believe its impossible because every where we look it seems to be increasing. Although Exapno Mapcase’s cite regarding the Lander limit might demonstrate the sort of proof I was looking for, so long as it doesn’t assume the second law as part of the calculation.

7

So, you accept that reversing causality is impossible, but you’re unconvinced that reversing entropy is impossible? But those are exactly the same thing.

8

Can you explain this more.

9

I think the point of Maxwell’s Demon, is that you have to be careful to consider all the elements of your system when applying thermodynamic principles, or you may slip into error. Otherwise you may have to make assumptions, and your solutions may be approximate.

In the case of Maxwell’s Demon, the original proposal failed to consider the Demon as part of the system it was interacting with. When you pretend that the Demon is not part of the system, it seems fairly obvious that the system could decrease in entropy. When you consider it as part of the system, (and if you assume it has to use energy to do work in the system, which is pretty much the definition of work) it is no longer clear that entropy will decrease. But now it’s the job of Maxwell or some other proponent to devise a demon that could do the job with less work than the entropy gained (speaking casually). It’s not at all clear that this could be done (and I’m guessing nobody has done it even theoretically, or we’d hear about it. Exapno Mapcase’s post cites a case of someone who has apparently disproven Maxwell’s Demon on even theoretical basis.

The creationist position that life defies the second law, as complexity of molecules and organisms increases over time is similar. It considers the biosphere as a closed system, ignoring the vast energy input of the sun (our own giant Maxwell’s Demon.

Lastly, answering the last part of your OP: if you could build a Demon that could accomplish the task, then I do believe that would require a major rewrite of thermodynamics, not just a paper-over fix of “except for Demon”.

BTW- I am not an expert, but I think that Thermodynamics has a VERY solid foundation. On this site , there are frequent expressions about the very high degree of experimental the Theory of Relativity and of The Standard Model. I think Thermodynamics is living in the same neighborhood.

10

Here are examples of theoretical and real molecular ratchets. These are essentially Maxwell’s Demons. Except apparently they don’t violate Second Law.

11

When we say that cause precedes effect, what we’re really saying is that low-entropy states precede high-entropy states. All of the “arrows of time” that we experience on a human scale are just different manifestations of the thermodynamic arrow, that entropy increases with time.

12

While it is clearly the case that cause precedes effect (i.e. there is a causal arrow of time) and that low entropy states precede high entropy states (i.e. there is a thermodynamic arrow of time), it’s not so clear to me that the former is a consequence of the latter, as I understand you to be saying.

I cannot speak for its validity, but see, for example, this paper for those of you lucky enough to have access to Phys. Rev. E. Relevant quote from the abstract:

In other words, the thermodynamic arrow of time, they claim, is a consequence of the causal arrow of time. Is that not the converse of what you’re arguing above, or have I just misunderstood you?

13

Most of the laws of physics are symmetric in time — the events in a film played in reverse still obey the Laws. The single notable exception is the Second Law of Thermodynamics. If we assume all physical laws are symmetric in time’s direction, then the Second Law (statistically tomorrow will almost certainly have more entropy than yesterday) should also work in reverse (yesterday should have more entropy than tomorrow!)

Many physicists accept that the Second Law results from a “boundary condition” — the extremely low entropy 13 billion years ago. As Chronos implies, all of time’s arrows, including human volition, point away from the Big Bang.

And physicists as early as Ludwig Boltzmann have speculated that entropy flow might be reversed if different boundary conditions are assumed. Would any physical laws (besides the circular 2nd Law) be violated if macroscopic entropy flow is not always unidirectional?

14

My understanding of the is the information theory says that information and energy equivalent. A demon adding information to the system (by sorting the atoms according to their velocity) is no more feasible than if it was magically creating energy.

15

And, of course, Maxwell-like demons (that don’t violate the 2nd Law) are ubiquitous in evolved organisms. The ion pumps that maintain the concentration gradient across organic cell membranes are pretty much exactly like Maxwell’s demon; except of course the they burn energy (ATP) - so the entropy of the organism is lowered, but waste heat increases the entropy of the environment.

The enzyme that makes ATP is another cool demon that lowers entropy locally - it even has a rotor, although of course it’s not a Brownian Ratchet, it’s driven by the proton gradient across a membrane, itself generated by the electron transport chain.

16

I think it’s important to point out that the article Exapno cites isn’t just one voice crying out in the wilderness against demons, but the starting point of an entire chain of thoughts and speculations. There were a great many follow-up articles and papers treating of this aspect of information vs. entropy in the literature, with some clever work-arounds to try to “save” the demon rather than exorcise it.
Here’s review of a 1990 book devoted to the topic (with a hefty $75 price tag):

http://aapt.scitation.org/doi/abs/10.1119/1.16914

Interesting sidenote: actual Maxwell’s Demon experiment from last year

17

It might help to understand that entropy, fundamentally, is a measure of information. Yes, I know that you’ve heard it described as “disorder”, and that seems opposed to information, but really, it isn’t. Consider, for instance, a set of moveable type, like you’d use in a printing press. When it’s not being used, the printer keeps it all sorted away in a tidy little cabinet, with a drawer for each letter: All of the 'a’s in one fairly large drawer, all of the 'b’s in the smaller drawer next to it, then all of the 'c’s, etc., all the way to a small drawer at the end for the 'z’s. That’s a low-entropy state, and it carries very little information. Now imagine that the printer is making a newspaper: He takes those letters out of their nice neat drawers, and arranges them in particular ways, to tell people about a hurricane. Or about a celebrity getting married. Or about a declaration of war, or about humans landing on the Moon, or about any other newsworthy subject. Now, there’s a lot of information.

Another example: I’m in charge of organizing my church’s library. After a lot of work, I’ve managed to get all of the books sorted, in alphabetical order by author’s name. If I want to describe where all of the books are, all I need to say is “they’re in alphabetical order by author’s name”. But now suppose a toddler gets into the room and messes everything up, with books strewn everywhere. If a volunteer went in to clean things up, I could tell them “put everything in alphabetical order by author’s name”, and (with a lot of work), they could exactly reproduce the original arrangement, just from that one simple instruction. But then what if I wanted to reproduce the mess? I could say “make a mess”, which is also a simple instruction, but if I did that, it’d end up as an entirely different mess. If I wanted to recreate exactly the same mess, I’d have to give a lot of information: I’d have to say things like “Huck Finn is on the center table, face down, six inches from the north edge and four inches from the west edge, with the top edge of the book oriented at 73º from north”, and then repeat for all of the thousands of other books in the library. The mess is more entropic than the sorted state, and what I mean by saying that is exactly that the mess requires more information to describe it.

18

The second law is just a probability, though. It is more likely that you end up in a higher entropy state than what you started in. While unlikely, it is not impossible to end up in a lower entropy state.

If the many worlds interpretation of QM is correct, and there is a universe for every possible state, then there is a universe where you dropped an egg on the floor, where it cracked and spread out all over, and then reassembled itself and hopped into your hand. This happens in 1 out of 10^googleplex or so universes.

In some universe, you built a “maxwell’s demon”, put it into a tank with a mix of red and blue food dye, and it separated the two colors through your demon’s membrane. I’m thinking the probability here is something like 10^graham’s number. When you show it off to your friends, in most universes, it doesn’t work, but in that improbable one, it does. Of course, it becomes more improbable every instant it is “running”, but in something like 1 out of 10^tree(3) universes, it would act somewhat consistently.

None of this would change the laws of physics, and would be entirely allowed, just rather unlikely. Physicist who watched your maxwell’s demon at play would scratch their heads and wonder what they got wrong, but not that many of them, compared to the countless number of worlds where the physicist just watch as you fail at your demonstration.

In one out of 10^tree(graham’s number) universes, this maxwell demon is a manufactured device that consistently works to separate liquids or gasses. In all of these universes, it would be exactly as likely for the effect to happen spontaneously, without the use of your manufactured device. In these universes, physics would be the same, and we would not need an sort of re-writing to account for the behavior, but if you actually lived in one of them, you’d probably be tempted to come up with a physical law to describe the improbable behavior, just as if you were playing poker, and kept getting dealt a royal flush, you may think that there is some reason why that happens, other than just pure chance.

There really is nothing saying the the entropy of a local system has to go up, just that it pretty much always does. It would not violate any laws for entropy to decrease in a local area for a brief time, it is just not likely to happen. One of the speculations of the big bang was that it came out of a transient and unlikely dip in entropy in a local area.

19

I thought that it might be this sort of argument. To me this seems to be dodging the question. You are defining cause and effect using entropy. You have moved the question to why defining cause and effect using entropy makes sense.

20

That’s the only way cause and effect have ever been defined. Go ahead, try to define them in any way that doesn’t come back to entropy or information (which is the same thing).