This question is about James Clerk Maxwell’s thought experiment, where he came up with the possibility of violating the second law of thermodynamics by imagining a sort of demon that could control a small door between two chambers containing gas with identical properties. The imaginary demon, however, can manipulate the door in such a manner that he will allow the fast molecules of gas to gather in one chamber, and the slow ones in the other, thus causing one chamber to warm up and the other to cool down, which would violate the second law of thermodynamics due to the resulting lower entropy.
I’m not sure I have understood this thought experiment very well (since science is not my strongest point) but I wonder if entropy could actually decrease if the demon were not a “finite being” (as described by James Clerk Maxwell himself), but an “infinite” one, who could generate its own energy limitlessly without making use of any source of energy either within the system or outside it (i.e. the universe). Could this non-finite being make a “better” demon and actually fulfill the violation of the second law of thermodynamics by decreasing the entropy?
You are reading too much into the name of this thought experiment (one of several, like Feynman’s ratchet, showing how the second law of thermodynamics works at a statistical mechanical level, the relationship between thermodynamic and information-theoretical entropy, and physical constraints on micro and macroscopic mechanisms and devices). Maxwell’s Demon is not a real guy. If you accidentally summon a real demon, sure they can generate infinite energy and violate entropy constraints, but IME initially you’ll have your hands full just keeping it from ripping your head off. Eventually, if you have a good relationship, it might oblige you by occasionally materializing a round of drinks out of thin air and inviting you to the best Walpurgis parties, but make sure you have a good handle on your soul; most people don’t.
If the demon can summon energy into the system, then of course it can move heat from one side to the other. That’s what an air conditioner does, after all.
A non-magical air conditioner uses low entropy electricity and turns it into high-entropy heat (so the hot side gets hotter than the cold side gets cold), which means overall entropy increases, when you include the outside source of power.
If your demon doesn’t need a power source and doesn’t create heat when it does work, then yes entropy will decrease. But in that case you’re just asking 'Can a magical demon do magic?"
The funny thing (for me) is that the other day I had a morning dream where I might have encountered the guy. I woke with a hangover.
I know, but I was wondering whether there are other aspects that my non-science oriented mind might have overlooked. Take the average speed, example, which plays an important role in this experiment. To separate faster-than-average particles from slower-than-average ones, I guess the demon is supposed to be able to do instantaneous measurements and to actually carry them out. The speed of each particle must constantly change due to the innumerable collisions, but the total energy of all the particles within the two chambers must remain constant. Does that mean the average speed stay the same as well?
Also, we know an omnipotent being cannot create a stone it cannot lift. Similarly, there may be logical or objective impediments that could prevent the demon from violating the second law of thermodynamics, despite his supernatural abilities.
Here an experiment is described where they purport to have constructed a Maxwell’s Demon and converted information to free (available) energy. The thing is, if the Demon had access to an infinite reserve of entropy/energy (physically impossible!?) and you performed Maxwell’s experiment, the Second Law of thermodynamics would still not be (directly) violated since all it needs to do is tap into its infernal infinite reservoir a little in order to accomplish its task. In real life, of course, there is no infinite cold sink or perpetual energy generator, there is an entropy cost to and a physical limit on computation, and so on.
It doesn’t work with a non-finite being IMO. An infinite being could bypass or change the laws of physics and so it isn’t a true challenge of the 2nd law
For further insights on managing your own personal demon, see Practical Demonkeeping, by Christopher Moore, an absurdist novel about a seminary student who accidentally summons a demon and then spends the next 70-some years of his life trying to get rid of him. The demon doesn’t rip his head off, but has the inconvenient habit of eating most of the other people they encounter.
And I initially thought that the only true challenge of the second law of thermodynamics would occur by means of a non-finite being.
If this objection to my idea is a valid one, then we should be able to generalize and state that no supernatural being belonging to a divine realm would break the law of physics if they performed any of their wonders in our world. And this is true, I wonder who would. Probably no one.
I remember the famous statement: “Colorless green ideas sleep furiously.”, which doesn’t make sense despite its apparently correct grammar. If we analyze the deep grammar of the sentence, however, it will be easy for us to see that its meaninglessness comes from the fact that this sentence actually does break grammar rules.
Maxwell’s thought experiment seems to work the same. If Wittgenstein’s statement has no reference to reality because he intentionally broke the rules of grammar to produce a nonsensical sentence despite its illusory correctness, then Maxwell also intentionally broke the rules of physics (in an eidetic manner) to produce a nonsensical experiment despite its illusory prospect.
In the linked experiment, the “door” is an electric field potential and doesn’t take energy to switch, but ultimately the computer is plugged into the mains.
I can roll with that. In other words, no miracle can break the laws of physics, since they are by definition supernaturally miraculous and not worked via physical means.
It seems I have been working with David Hume’s definition where miracles were regarded as violations of the laws of nature. If miracles and laws of nature belong to separate realms, I wonder then why Maxwell chose to devise his thought experiment.
There are, I think, only two possibilities: the demon measures the speed of the particles and operates the door (1) by making use of energy available in our physical world, or (2) by using energy available outside our physical world (which he can either access or produce). Apparently, neither (1) not (2) breaks the laws of physics, which makes me wonder then about the purpose and utility of Maxwell’s thought experiment.
Firstly, the point of a thought experiment is to extrapolate out the implications of some idea or model, as an aid to understanding or to illustrate an issue with the model. Thinking about whether it’s viable in the real world is largely the point, as the conclusion may have important implications.
But, secondly, it’s not actually true that the case (1) does not violate the laws of the physical world as we currently understand them. A real life opening and closing machine made of matter could not actually reverse entropy without input of external energy.
Surprisingly, the issue is not with the energy of opening and closing the gate. According to this PBS space time video, the demon / machine’s “brain” will need to be a finite state system of some type, and that system’s changes (particularly “resetting”) will necessarily be larger than the energy gain of selectively letting particles through.
I confess though, I don’t completely follow this myself. But anyway, they are summarizing the consensus view of theoretical physicists.
Thirdly, the case (2) is really fighting the terms of the hypothetical itself. If the only way we can get Maxwell’s demon to save energy is by allowing infinite energy to come from the 11th dimension, then rather than refuting the hypothetical it shows exactly the thing the hypothetical was aimed at demonstrating.
Finally, and this is not related to your post, we know that spontaneous entropy reversals can indeed happen; they are just fantastically unlikely. So we don’t really need the demon as such. Entropy is just an important principle when we’re talking about numbers of years small enough to write on paper using standard notation (raised powers).
If we’re talking ridiculous timescales, which is A-OK from a philosophy point of view, we can have arbitrarily big entropy reversals.
Oh, I see. And it is some of these implications that I would like to grasp (of course if my limited abilities allow me to really understand anything).
So, we have the case where Maxwell’s “finite being” would violate the laws of physics if he really managed to separate the fast particles from the slow ones (and thus decreasing the entropy of the system) without increasing the entropy of the universe.
We can also have the case where the demon did not belong to our physical world and could access energy available outside the universe, which can only be a fairy-tale hypothesis that implicitly proves physical law violations are not possible and explicitly shows the demon will not violate any physical laws since they do not apply to him and he is not supposed to observe them.
I guess that ultimately the reason why it would be difficult for a natural “demon” to decrease the entropy in the system imagined by Maxwell is that enormous amounts of energy are necessary to achieve this feat, which would lead to an increase in the total entropy of the universe.
But the spontaneous entropy reversal you mention seems to refer exactly to this natural “demon”, whose existence we have just agreed would violate the laws of physics. :eek:
IANA Physicist, so possibly someone like Chronos might correct this, but AIUI:
…this is all correct.
I guess that for entropy, we have to make the distinction between practically possible and technically possible.
The laws of thermodynamics and entropy were realized around about the industrial revolution; an appreciation of not only the limits of what we could engineer but the limits of what could be engineered, period. And those limits are still understood to be entirely true. We can’t sidestep these laws.
But technically-speaking, the universe itself will periodically reverse entropy just by random chance. But you’d have to wait trillions of times the universe’s current age just to have even odds of seeing a cubic meter of air at equilibrium spontaneously separate out into a warm and cool side. So in a sense it’s the ultimate in pedantry.
He was not saying anything about modern-day supernatural beings like trying to work out how many of them can dance on the head of a pin. He was opening up a line of inquiry into the limitations of real-life devices. It forces us to think about the non-trivial issues of how to possibly construct a mechanism that does what the demon does (there is experimental work on this, like the “information-powered refrigerator”) and why its operation cannot in fact violate the laws of thermodynamics. It is related to Landauer’s Principle and similar information-theoretic physical limits, for example.
Practically speaking, what Maxwell was saying was “Suppose we have some mechanism for measuring particles and opening and closing the door, and don’t worry too much about the details of the mechanism”. If Maxwell were writing today, he’d surely have described the mechanism as a robot or a computer. But he didn’t know of robots nor computers, so he instead used a scientifically-undefined term for the operator of his mechanism.
With a sealed, contained room of gas, yes, this is true, the entropy of the box will eventually (for very large values of “eventually”) decrease in such a way. But it’s a common mistake to think that this will (for even larger values of “eventually”) happen to the Universe as a whole. But it won’t: The probability of it happening in any given interval of time is not constant, and is in fact decreasing with time, sufficiently quickly that the probability of it ever happening, even with truly infinite time, is incalculably close to zero.