Maxwell's Demon

Maxwell’s Demon is a fascinating theoretical problem (I guess it’s really a paradox) in classical thermodynamics. I’m sure that the many physicists who log in here know the details of the paradox…so I’ll only summarize it…

Imagine that you have two chambers that each contain X number of molecules at equal temperatures (average kinetic energy). Between the chambers there is a “trapdoor” that is operated by a “demon” that can perceive when a high energy molecule is moving towards the trapdoor. He can open the trapdoor when it is about to be struck by the molecule, allowing it to pass into the other chamber. If he decides not to open the trapdoor, the molecule will be reflected back into its own chamber.

The problem is that if such a demon can exist, he could allow only fast moving molecules into one chamber, thus creating a temperature difference between the two chambers. This would violate the second law of thermodynamics.

I understand that several explanations have been offered to explain this apparent paradox and preserve the Second Law (which seems to be one of the very few physical “laws” that are absolutely “true.” For example, you could argue on statistical grounds that the demon could have only a marginal effect… beyond a certain point there would be an increased probability that when he opened the door to let a high energy molecule through, a high energy molecule would be approaching the door from the other side, which would negate his ability to change the temperature difference between the two chambers.

You could also argue that the demon would have to exist on such a small scale that quantum effects, especially the Uncertainty Principle, would render the demon ineffectual.

I suggest that Maxwell’s Demon can be allowed to exist and could be allowed the ability to do what Maxwell wanted him to do, without any violation of the Second Law. I propose that the apparent paradox disappears if we consider the association of entropy with the complex organization of matter, i.e., that material complexity is inversely related to entropy.

For the demon to function as postulated, he must be able to make decisions…that is, he must display some form of perception and consciousness. In order to do that, he must be complex. As such, his presence in one of the chambers must affect the value of the entropy assigned to his chamber. The demon cannot exist simultaneously at both sides of the door…he must be in one chamber or the other.

Perception and consciousness are behaviors that depend upon the existence of organized matter.

The presence of the demon in one of the chambers significantly lowers the entropy of that chamber. This difference in entropy would allow the demon to significantly raise the temperature of the chamber he is not in, but only up to the point that the temperature change is balanced by the demand that dS>0.

Thus, if you consider the affect of the demon’s complexity on the entropy of the universe of the two chambers, you can accept his presence and effectiveness in creating the temperature difference, without there being any paradox or violation of the Second Law.

I am not a professional physicist, and I’m aware that there are plenty of goofy and stupid ideas that amateurs have proposed. This may be one of those, but I’d be interested in some feedback from others who read this Board.

I am unable to find any column by Cecil on this subject.

It’s not the entropy of the demon that matters, but the change in entropy of the demon over time (and the change in entropy of the rest of the system). Besides, it is possible for the demon to be neither in one side nor the other, but controlling the window from outside.

This is my understanding of how it works. In order to tell if an approaching molecule will hit the window, and whether he should let it through the window, the demon has to perform calculations. In order to perform calculations he has to have some kind of memory, like a computer (or a human brain). Theoretically it is possible to remember a bit of information without a change of entropy. But since he has a finite amount of memory, he will eventually have to erase and overwrite a memory space. It is the process of forgetting the memory that requires an increase in entropy, at least balancing the reduction of the entropy of the system minus the demon. If I remember right, the theoretical minimum increase in entropy for forgetting one bit of information is Boltzman’s constant times the natural logarithm of two, k ln 2.

This is what I learned from reading Feynman Lectures on Computation by Richard Feynman. I’ll be the first to admit I’m not sure I entirely understood the book.

What if the demon wasn’t in either room, but was in a third chamber where it could still perceive the energy of the molecules.
It would use some sort of remote door opener as well.

Just my £0.02

atarian
PS: It’s probably obvious I’m not a physicist.

Welcome to the SDMB, and thank you for posting your comment.

Are you referring to any Straight Dope column? If not, this thread will be moved to another forum.


moderator, «Comments on Cecil’s Columns»

Sorry…my post was NOT a comment on any of Cecil’s Columns. Please feel free to move it elsewhere.

Sincerely,

Neurodoc.

Maxwell’s thought experiment does not constitute a paradox. If a setup such as he describes did work, this would contravene the Second Law. However, while this would serve to make us thermodynamicists less smug, it would have no theoretical implications, as the Second Law is entirely empirical.

The correct explanation has not been given here yet for why this system won’t actually work (and it’s better not to think of a real living tiny demon. It makes no difference to the problem and only confuses matters).

The mechanism has to identify suitable molecules, and open and close a trapdoor at appropriate moments. To identify suitable molecules, it has to shine a light on them and view the reflected radiation. The light adds energy to the system and the entropy increase is greater than any entropy decrease that arises from the segregation of the molecules. In effect you are heating up the cold side more than the hot side.

OK, then, two demons.

I think Feynman talked about the Maxwell demon thing in his red book lectures, let’s see, yes, v.I, 45-5

He claims that the simplest demon is just a ratchet and pawl setup, which he had discussed previously. The mechanism gets so hot that it doesn’t work right.

I was a physics major for 2 years in the late 80s and early 90s without being exposed to the explanation of Maxwell’s Demon I described above. I was given the same explanation you gave. I first came across the new explanation in The Quark and the Jaguar by Murray Gell-Mann, but I had a hard time believing it. p. 223

I was finally convinced by the more technical explanation found in Feynman Lectures on Computation by Richard P. Feynman, Edited by Anthony J. G. Hey and Robin W. Allen. The technical stuff leads up to the following passage on pages 149-150

Among other works in the field, Bennett wrote “Thermodynamics of Computation–A Review” by Charles H. Bennet International Journal of Theoretical Physics 21, 905 (1982)

Moving this to General Questions. It’s a good thread, Neurodoc, just slightly misplaced. Feel free to look around at the other GQ threads, as there’s a good chance that you’ll find several interesting.

I don’t think you understand what entropy is. Every object has positive entropy. Ordered objects have less entropy than unordered objects, so a “demon” would have less entropy than just a puddle of organic compounds, but it would still have positive entropy. Putting a demon in the room would increase the entropy. However, this isn’t really relevant, since whatever change introducing the demon may cause, it will be reversed when the demon is removed at the end.

Yeah, espescially if you consider how demons typically behave when you put them in rooms. Maxwell’s Angel, well there’s a different problem entirely.

Thanks for the replies. As regards “positive” and “negative” entropy & the comment that anything, including the demon, would increase the entropy of the chamber, my point was simply that the demon proposed by Maxwell would have to be able to perceive the approaching molecules, determine their velocity, and operate, through some physical linkage, the gate between the chambers…in order to do what Maxwell proposed he could do.

I am aware of Feynmann’s ratchet-demon, and I don’t think it explains the paradox. For one thing, the ratchet-demon depends upon a mechanical analogy and a sort of spring trap that is set at a specific tension to open the door via a mechanical likage when a high-momentum molecule strikes the door. The problem with this sort of demon is that he can’t really effect an entropy change between the two chambers. The reason is that he has no real perceptual ability. The demon proposed by Maxwell is a conscious demon. The ratchet demon would not be able to effect an entropy change beyond a certain “noise level” between the chambers because of the statistical likelihood that after a point when the door was tripped open to admit a high-energy molecule there would be another molecule on the other side that would be let in, thus neutralizing the effect.

In any case, my argument was very simple. An effective conscious demon installed on one side of the gate would have to be complexly organized. His complex organization would have to be accounted for in the calculation of the initial entropy values of the two chambers. My argument is that when you make this calculation, there is a significant difference in the entropy between the two chambers, such that the demon would be allowed to raise the temperature of the other chamber significantly, WITHOUT VIOLATING THE 2nd LAW. The amount of the temperature increase would be determined by the amount of complexity of the demon, and the effect of that complexity on the initiaL entropy calculations for the two chambers.

Well, first off, if you apply any sort of immeasurable “Magical X” to a problem, you’re bound to get a paradox.

Think of it this way: “I’ve got a magical stone that can violate the 2nd Law of Physics. Wouldn’t that violate the 2nd Law of Physics, thus rendering it untrue?” You can provide any sort of impossible influence on a problem to reach any conclusion you like.

However, I understand the notion of “Only high-energy particles are allowed to pass.” I just wanted to pick what I saw as a very big nit.

Second, doesn’t the 2nd Law only apply to Closed Systems? That is, a system that’s not being influenced by an external source? Seems that a “demon” (or angel, or funk-a-tronic machine, or a guy named Bert) would be an external influence on the system, thusly making any comment about the 2nd Law unnecessary.

(Here’s hoping that the OP didn’t go completely over my head…)

For the record, LArry Niven had something like this in one of his short story collections…

I never really got it till now.

Thanks!!

The problem with that reason is that you haven’t defined consciousness yet. Bwha hahahahaha

Just a note - there is a little curiosity called a Hilsch vortex tube which I saw in some hobbyist magazine years ago under the title “Chain Maxwell’s Demon”. It doesn’t, really, nor does it violate any laws of thermodynamics, but it is a cute demonstration of a device which separates hot and cold air with no moving parts:

http://keller.physics.oberlin.edu/catalog/demonstrations/vortextube.html

Of course, energy is being put into this system to accomplish the separation because you have a source of compressed air.

Niven’s story is a VERY short one, basically a setup for a one-liner deserving of a rimshot from a drummer in the background. It is called “Unfinished Story #1”, and one place it may be found is in the “All the Myriad Ways” collection.