Maxwell s Demon

The earliest hint that physics and information might be more than just casually related actually dates back at least as far as 1871 and the publication of James Clerk Maxwell s Theory of Heat, in which Maxwell introduced what has become known as the paradox of Maxwell s Demon. Maxwell postulated the existence of a hypothetical demon that positions himself by a hole separating two vessels, say A and B. While the vessels start out being at the same temperature, the demon selectively opens the hole only to either pass faster molecules from A to B or to pass slower molecules from B to A. Since this results in a systematic increase in B s temperature and a lowering of A s, it appears as though Maxwell s demon s actions violate the second law of thermodynamics the total entropy of any physical system can only increase, or, for totally reversible processes, remain the same it can never decrease. Maxwell was thus the first to recognize a connection between the thermodynamical properties of a gas (temperature, entropy, etc.) and the statistical properties of its constituent molecules. 

Ieff90] LefF, H.S, and A.F.Rex, editors. Maxwell s Demon entropy, information, computing, Princeton University Press, 1990. 

A Gibbs angel, like Maxwell s demon, unfortunately does not exist. Neither is there at present an experimental technique to achieve what could be accomplished by a Gibbs angel. Hence, one has to try to build up a picture of the structure of the interface by letting the mind play with the other types of cruder information that are available. 

For good accounts of the history and meaning of the concept of entropy, see (a), (b) (a) von Baeyer HC (1998) Maxwell s demon. Why warmth disperses and time passes. Random House, New York, (b) Greenstein G (1998) Portraits of discovery. Profiles in scientific genius, chapter 2 ( Ludwig Boltzmann and the second law of thermodynamics ), Wiley, New York... 

There are relationships between thermodynamic and informational entropy. For example, the well-known Maxwell s demon, which reverses thermodynamic entropy with information, but getting that information exactly balances out the thermodynamic gain the demon would otherwise achieve. 

One spectacular use of a rotaxane was to illustrate James Clerk Maxwell s 19th century thought experiment known as Maxwell s demon as shown in Fig. 1.23. Maxwell proposed several experiments that would violate the Second Law of Thermodynamics to show how the entropy of an isolated system could be reduced without expending energy. To do so he invoked the idea of a demon who effortlessly operates a frictionless door between two compartments which contain particles at different temperatures. Whenever a particle approaches the door the demon decides whether to open it and allow the particle through. In this way the particles can be sorted so that one compartment contains only hot particles and the other only cold. A similar example can be envisaged in which particles at an equilibrium pressure are moved from one compartment to the other to increase its pressure without any work apparently being done. 

Fig. 1.23 Maxwell s demon demonstrated by an irreversible rotaxane interconversion [80]...

Third, what is the dynamical origin of Maxwell s demon As is well known since the work of Maxwell, Szilard, and Brillouin, nonequilibrium conditions are necessary for systems to do information processing. Therefore, in studying biochemical reactions, we are interested in how nonequilibiium conditions are maintained at the molecular level. From the viewpoint of dynamics, in particular, the following problem stands out as crucial Does any intrinsic mechanism of dynamics exist which helps to maintain nonequilibrium conditions in reaction processes In other words, are there any reactions in which nonergodicity plays an essential role for systems to exhibit functional behavior ... 

These monomers are not just disappearing off the face of the earth, into the black hole in our clothes dryers that manages to selectively consume just one of the members of each pair of socks we own. (We now buy identical socks to thwart this incarnation of Maxwell s demon ) They are actually going into the polymer chains that are being formed at that instant of time. The ratio of these two equations must therefore represent the ratio of monomer 1 to monomer 2 incorporated into the chains at that moment. 

If you are interested in the history of this subject one cannot do better than read Maxwell s Demon,... 

We also took this example from Maxwell s Demon, H. C. von Baeyer, Random House, 199S. 

Maxwell s demon provided a basis for a great deal of discussion on a spurious issue, i.e., the relation between thermodynamics and "free will." Was there a connection between the heat death of the universe and the exercise of free will This issue died away as it became apparent that the thing which distinguished the demon was superior information, not a will or desire. 

The fundamental stability conditions in thermodynamics are formulated as variational principles. Within the zero-temperature canonical ensemble, the quantities n and V are used to specify the state of interest. Suppose one chooses a nonoptimum pressure, P(r). For example, we can divide the system with a partition and place Maxwell s demon at the door between the partitions to ensure that the pressure on one side of the partition is greater than that on the other side of the partition. Then, we have that ... 

The concept of Maxwell s demon plays a role in the thermodynamics of computation [15]. The views concerning the role of Maxwell s demon are still controversial. 

Bub, J. Maxwell s demon and the thermodynamics of computation. Stud. Hist. Philos. Sd. B Stud. Hist. Philos. Mod. Phys. 32(4), 569-579 (2001)... 

The heart of our trick will be to utilize explicitly a Maxwell s demon to break up a very large cluster of size g and make it back into a monomer. As we remarked before, in the ph ical nucleation experiment these large clusters never really form and so the results obtained do not really utilize the demon. 

C. W. F. McClare, Chemical Machines, Maxwell s Demon and Living organisms, J. Theor. Biol. 30, 1-34 (1971). 

Bennett CH Notes on Landauer s principle, reversible computation, and Maxwell s Demon. Studies in History and Philosophy of Modern Physics 2003, 34(3) 501-510. 

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