I’ve always been fascinated by the famous Maxwell’s Demon Paradox…you know the problem: there is this tiny Demon that controls a little gate between two chambers in which there are a finite number of paricles at the same temperature (i.e. average kinetic energy). This crafty little Demon is situated in one chamber and can open and close the gate at will to let a molecule pass into the other side. According to the paradox, he should be able to open the gate for fast molecules, and eventually this will lead to a preponderance of higher energy particles in the other chamber. This will result in a higher temperature in the other chamber and a spontaneous degrease in the entropy of the Universe (consisting of the two chambers) in violation of the Second Law of Thermodynamics.
There have been all sorts of explanations as to why the 2ND Law is not violated, including quantum physical arguments that were completely unknown to Maxwell, and which seem to be irrelevant to Classical Thermodynamics.
One argument that I think can be made entirely within the frame of classical thermodynamics is that the Demon, in order to function as required by the paradox, would have to be capable of perception and conscious behavior in order to “decide” when and when not to open the gate. Such a Demon must be in one chamber or the the other (he can’t be in both at the same time) and would have to be of complex structure. His presence as a complex structure in one of the chambers would affect the entropy value in his chamber (by significantly lowering it). Thus, classical thermodynamics would allow him to effect a change in the temperatures of the two chambers, but only so far as his organized structure would allow when factored into the equations of state between the two chambers. This would lead to the “spontaneous” change in temperature without any violation of the 2nd Law, so that the paradox is only apparent and not real.
The change in temperature will be limited by the negative entropic contribution of the Demon in his chamber. From a kinetic/statistical point of view it will also be limited by the Demon’s ability to perceive only molecules on his side of the gate. At some point after letting high-energy particles through to the other side, when he opens the gate to another selected high speed particle there will be an unseen high speed particle entering from the other side.
The nice thing about these arguments is that they effectively deal with the paradox without having to resort to Heisenberg’s Uncertainty Principle, quantum theory, or anything else besides good old thermodynamics.
There are no violations of the laws of thermodynamics simply because work IS being done in the seperation of the molecules. The demon has to put energy into the system when opening and closing his valve. This is in actual fact no more and no less than what happens in a typical air conditioner. An air conditioner is an electro-mechanical device for pulling energy from the air and dumping it in another place. Energy must be input to drive the compressor . The compression/expansion cycle of the coolant takes th place of Maxwell’s Demon.
There is a device referred to sometimes as Maxwell’s Demon. This device is more properly known as a Hilsch vortex tube. The tube has two arms of unequal length connected to the sides of a spiral shaped chamber. On the side with the short arm, the chamber exit is small. The exit on the side with the long arm is as large as the chamber itself. Compressed air is injected into the chamber at the widest part. If everything is adjusted right, hot air comes out of one of the arms, and cold air comes out of the other.
I appreciate the argument that the demon expends some energy in opening/closing the gate. I assume that the great genuis J.C. Maxwell also would have appreciated this argument. That consideration, however, does not really answer the paradox, which has to do with the spontaneous entropy change between the two chambers effected by the demon. You may give this demon a certain amount of free energy to do the work required to control the gate and include that energy in your calculations. The problem is that you cannot explain his ability to act as a demon without giving him a LOT of unexplainable free energy. You can see this problem by trying to imagine a simple mechanism whereby the demon operates. Heat pump and refrigeration mechanisms, including the one you mention, are easily explained, and Maxwell would have had no problem understanding how they work.
The best explanation for the paradox, in my opinion, is what I said it was: i.e., that the demon would have to be conscious, and that a conscious “mechanism” would have to be so complex that its complex organization would so reduce the entropy in its chamber that any change in temperature between the two chambers would not violate the 2nd Law. This, I believe, is a novel argument, and a compelling one.-
Is there some special organizing principle in living beings, some entity that manages to create order in the liquid pandemonium of atoms and molecules? About 150 years ago, the physicist Maxwell, while musing about the laws that rule the tumultuous molecular world, came up with an intriguing idea. He conceived an experiment, a thought experiment, in which a little demon who picks out molecules seemed to escape what was thought to be the supreme law, the second law of thermodynamics. This demon comes as close as anything to the organizing biological principle we are angling for. So, let's take a look at that gedankenexperiment.
Maxwell chose a system made of just two sorts of molecules, a mix of hot and cold gas molecules moving randomly in two chambers, A and B, connected by a friction-free trap door (Fig. 1.1). Suppose, said Maxwell, we have a demon at that door, who can see individual molecules and distinguish a hot molecule from a cold one. When he sees a hot one approaching from B to A, he opens the door and lets it through. As he repeats that operation over and over, we would wind up with an organization in which the two kinds of molecules are neatly sorted out into a hot and a cold compartment--an organization which would cost nothing because the demon only selects molecules but does no work.
One literally seemed to get something for nothing here. The assumption of a friction-free operation is valid in a thought experiment, because there is no intrinsic lower limit to performance. So, to all appearances, this cunning organizing entity of Maxwell's seemed to flout the Second Law. And adding insult to injury, it would be able to drive a machine without doing work--the old dream of the perpetual motion machine come true.
This paradox kept physicists on tenterhooks for half a century. Two generations of scientists tried their hands at solving it, though to no avail. The light at the end of the tunnel finally came when Leo Szilard showed that the demon's stunt really isn't free of charge. Though he spends no energy, he puts up a precious commodity called information. The unit of this commodity is the bit, and each time the demon chooses between a hot and a cold molecule, he shells out one bit of information for this cognitive act, precisely balancing the thermodynamics accounts.
Thus, the hocus-pocus here has an exact information price. As has happened often in physics, the encounter with a deep paradox led to a higher level of understanding. Szilard's introduction of the concept of information as a counterweight to thermodynamics disorder (entropy), opened a whole new perspective of the organization of energy and matter. It marked the beginning of information theory. This theory already has shown its pizzazz in a number of fields in physics and engineering; the present-day communication and computer revolution provides ample proof of that. But perhaps its greatest power lies in biology, for the organizing entities in living beings--the proteins and certain RNAs--are but Maxwell demons. They are the most cunning ones, as we shall see; their abilities of juggling information are so superlative that it boggles the mind.
and more related to this… http://www.well.com/user/hlr/texts/tft6.html
"In 1922, a Hungarian student of physics by the name of Leo Szilard (later to be von Neumann’s colleague in the Manhattan project), then in Berlin, finally solved the paradox of Maxwell’s demon by demonstrating that the demon does indeed need to contribute energy to the system, but like a good magician the demon does not expend that energy in its most visible activity–moving the gate–but in what it knows about the system. The demon is a part of the system, and it has to do some work in order to differentiate the hot and cold molecules at the proper time to open the gate. Simply by obtaining the information about molecules that it needs to know to operate the gate, the demon adds more entropy to the system than it subtracts.
Although Szilard showed implicitly that information and entropy were intimately connected, the explicit details of the relationship between these two qualities, expressed in the form of equations, and the generalization of that relationship to such diverse phenomena as electrical circuits and genetic codes, were not yet known. It was Claude Shannon who made information into a technical term, and that technical term has since changed the popular meaning of the word."
I was not aware of Szilard’s idea. It seems that I was suggesting more or less the same explanation. The Demon, in order to be able to process the required information and act upon it must be “conscious.” Not only must he exhibit “consciousness,” he must do so on a very small scale (molecular size). This means that his structure must be complex, probably more complex than would be physically possible, given the dimensions of atoms and molecules. But we may ignore that restriction and assume that such a complex demonic structure could exist in the physical demensions required for the Demon. Even if we assume this, the equations of Classical Thermodynamics would allow us to assign a “negative entropic value” to the Demon that would be calculated in the total entropy of his chamber, and would allow him to effect a “spontaneous” temperature difference between the chambers without violating the 2nd Law.
I just reviewed Szilard’s arguments,and I think I was saying the same thing, although I do think my presentation of the argument is a bit more clear than his.
One thing that I really like about Classical Thermodynamics is that its principles seem to have withstood the test of time and experimental scrutiny from the quantum to the galactic levels. This is quite amazing for a theory that is essentially empirical and based on common-sense macroscopic experience.
The only other scientific theory, in my opinion, that shares the success of Maxwell’s Classical Thermodynamics (especially the 2nd Law) is Darwin’s Theory of Natural Selection. These two theories seem to be profoundly true under any and all imaginable conditions anywhere and at every level of physical organization.
I think you may be making this more complicated than it needs to be. You need to remember that this was intended to be a Gedankenexperiment. Anthropomorphizing the “demon” blurs the fine point of the paradox which is that “information” about a system is not free and has a thermodynamic cost no matter how conceptualized.