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Chapter 2: Groups and Statistical Mechanics

A very important idea in statistical mechanics is that of the Maxwell demon. Let us suppose a gas in which the particles are moving around with the distribution of velocities in statistical equilibrium for a given temperature. For a perfect gas, this is the Maxwell distribution. Let this gas be contained in a rigid container with a wall across it, containing an opening spanned by a small gate, operated by a gatekeeper, either an anthropomorphic demon or a minute mechanism. When a particle of more than average velocity approaches the gate from compartment A or a particle of less than average velocity approaches the gate from compartment B, the gatekeeper opens the gate, and the particle passes through; but when a particle of less than average velocity approaches from compartment A or a particle of greater than average velocity approaches from compartment B, the gate is closed. In this way, the concentration of particles of high velocity is increased in compartment B and is decreased in compartment A. This produces an apparent decrease in entropy; so that if the two compartments are now connected by a heat engine, we seem to obtain a perpetual-motion machine of the second kind.

It is simpler to repel the question posed by the Maxwell demon than to answer it. Nothing is easier than to deny the possibility of such beings or structures. We shall actually find that Maxwell demons in the strictest sense cannot exist in a system in equilibrium, but if we accept this from the beginning, and do not try to demonstrate it, we shall miss an admirable opportunity to learn something about entropy and about possible physical, chemical, and biological systems.

For a Maxwell demon to act, it must receive information from approaching particles, concerning their velocity and point of impact on the wall. Whether these impulses involve a transfer of energy or not, they must involve a coupling of the demon and the gas. Now, the law of the increase of entropy applies to a completely isolated system, but does not apply to a non-isolated part of such a system. Accordingly, the only entropy which concerns us is that of the system gas-demon, and not that of the gas alone. The gas entropy is merely one term in the total entropy of the larger system. Can we find terms involving the demon as well which contribute to this total entropy?

Most certainly we can. The demon can only act on information received, and this information, as we shall see in the next chapter, represents a negative entropy. The information must be carried by some physical process, say some form of radiation. It may very well be that this information is carried at a very low energy level, and that the transfer of energy between particle and demon is for a considerable time far less significant than the transfer of information. However, under the quantum mechanics, it is impossible to obtain any information giving the position or the momentum of a particle, much less the two together, without a positive effect on the energy of the particle examined, exceeding a minimum dependent on the frequency of the light used for examination. Thus all coupling is strictly a coupling involving energy; and a system in statistical equilibrium is in equilibrium both in matters concerning entropy and those concerning energy. In the long run, the Maxwell demon is itself subject to a random motion corresponding to the temperature of its environment, and as Leibniz says of some of his monads, it receives a large number of small impressions, until it falls into "a certain vertigo," and is incapable of clear perceptions. In fact, it ceases to act as a Maxwell demon.

Nevertheless, there may be a quite appreciable interval of time before the demon is deconditioned, and this time may be so prolonged that we may speak of the active phase of the demon as metastable. There is no reason to suppose that metastable demons do not in fact exist; indeed, it may well be that enzymes are metastable Maxwell demons, decreasing entropy, perhaps not by the separation between fast and slow particles, but by some other equivalent process. We may well regard living organisms, such as Man himself, in this light. Certainly the enzyme and the living organism are alike metastable: the stable state of an enzyme is to be deconditioned, and the stable state of a living organism is to be dead. All catalysts are ultimately poisoned: they change rates of reaction, but not true equilibrium. Nevertheless, catalysts and Man alike have sufficiently definite states of metastability to deserve the recognition of these states as relatively permanent conditions.


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