Maxwell's demon

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Maxwell's demon is a character in an 1867 thought experiment by the Scottish physicist James Clerk Maxwell, meant to raise questions about the second law of thermodynamics. This law forbids (among other things) two bodies of equal temperature, brought in contact with each other and isolated from the rest of the Universe, from evolving to a state in which one of the two has a significantly higher temperature than the other. The second law is also expressed as the assertion that entropy never decreases.

Maxwell described his thought experiment in this way:

"... if we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are as essentially finite as our own, would be able to do what is impossible to us. For we have seen that molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower molecules to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics." [1]

In other words, Maxwell imagines two containers, A and B, filled with the same gas at equal temperatures, placed next to each other. A little "demon" guards a trapdoor between the two containers, observing the molecules on both sides. When a faster-than-average molecule from A flies towards the trapdoor, the demon opens it, and the molecule will fly from A to B. Thus, the average speed of the molecules in B will have increased, while the molecules in A will have slowed down on average. However, since average molecular speed corresponds to temperature, the temperature in A will have decreased and in B will have increased; this is contrary to the second law of thermodynamics.

Is Maxwell correct? Could such a demon, as he describes it, actually violate the second law? One of the most famous responses to this question was suggested in 1929 by Leó Szilárd and later by Léon Brillouin. Szilárd pointed out that a real-life Maxwell's demon would need to have some means of measuring molecular speed, and that the act of acquiring information would require an expenditure of energy. The second law states that the total entropy of an isolated system must increase. Since the demon and the gas are interacting, we must consider the total entropy of the gas and the demon combined. The expenditure of energy by the demon will cause an increase in the entropy of the demon, which will be larger than the lowering of the entropy of the gas. For example, if the demon is checking molecular positions using a flashlight, the flashlight battery is a low-entropy device, a chemical reaction waiting to happen. As its energy is used up emitting photons (whose entropy must now be counted as well!), the battery's chemical reaction will proceed and its entropy will increase, more than offsetting the decrease in the entropy of the gas.

Szilárd's insight was expanded upon in 1982 by Charles H. Bennett. In 1960, Rolf Landauer realized that certain measurements need not increase thermodynamic entropy as long as they were thermodynamically reversible. Due to the connection between thermodynamic entropy and information entropy, this also meant that the recorded measurement must not be erased. In other words, to determine what side of the gate a molecule must be on, the demon must store information about the state of the molecule. Eventually, the demon will run out of information storage space and must begin to erase the information that has been previously gathered. Erasing information is a thermodynamically irreversible process that increases the entropy of a system. [2].

Real-life versions of Maxwellian demons (with their entropy-lowering effects, of course, duly balanced by increase of entropy elsewhere) occur in living systems, such as the ion channels and pumps that make our nervous systems work, including the human brain. Single atom traps allow an experimenter to control the state of individual quanta in the same way as Maxwell's demon. Molecular-sized mechanisms are no longer found only in biology; they are also the subject of the emerging field of nanotechnology. A mechanical implementation exists as a commercially-available device, called a Ranque-Hilsch vortex tube. Due to conservation of angular momentum, hotter molecules are spun to the outside of a tube while cooler molecules spin in a tighter whirl within the tube, allowing venting of each from opposite ends of the tube.

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Maxwell's demon in popular culture

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See also

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External links and references

  • Harvey S. Leff, Andrew F. Rex (editors), Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing, Institute of Physics, 2003 — an anthology and comprehensive bibliography of academic papers pertaining to Maxwell's demon and related topics. Chapter 1 provides a historical overview of the demon's origin and solutions to the paradox. The 1st edition from 1990 (out of print) contained several additional relevant papers.
  • Charles H. Bennet, "Demons, Engines and the Second Law", Scientific American, pp.108-116 (November, 1987).
  • Richard P. Feynmann, "Feynman Lectures on Computation", Addison-Wesley, 1996, pp.148-150bg:Демон на Максуел

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