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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 possibility of violating second law of thermodynamics.

Maxwell's thought experiment

The Second Law of Thermodynamics 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 in an isolated system, entropy never decreases.

Maxwell described his thought experiment in this way[1]:

... 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.

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.

Criticism and development

Maxwell's thought experiment has troubled physicists ever since he first published it.

Is Maxwell correct?
Could such a demon, as he describes it, actually violate the second law?

Several physicists have presented calculations that show that the second law of thermodynamics will not actually be violated, if a more complete analysis is made of the whole system including the demon. The essence of the physical arguments is to show by calculation that any demon must "generate" more entropy segregating the molecules than it could ever eliminate by the method described.

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.

Put simply, no matter how it is done, both the act of the demon watching molecules and the act of opening and closing the trapdoor is by definition work and requires the expenditure of energy. These explanations, however, are inadequate as the concept of the demon is not stated and may work as described below in Alternate and Improved Demons.

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. Bennett showed that, however well prepared, eventually the demon will run out of information storage space and must begin to erase the information it has previously gathered. Erasing information is a thermodynamically irreversible process that increases the entropy of a system.[2]

Alternate and improved demons

Maxwell's demon could work this way: imagine a dividing wall in which each element would function as a valve set to allow only those particles of higher velocity/energy/enthalpy through into the other chamber. This would result in accumulation against the entropic gradient, apparently contrary to the second law. Not only would the "work" involved in separating the molecules take a small amount of energy to begin with, after analyzing the location of the molecule, the theoretical "demon" would have to forget the location of the molecule, which would expend more energy than would be created by the energy-generating action of the generator. Simply put, to forget is work by definition, and would prevent the engine from producing any amount of energy.

A slower process which would work just as well as Maxwell's would be a wall in which there was a single valve: by the law of random motion every particle would at some time or another impact this valve and be "assessed" by the valve mechanism and thus either pass through or not into the second chamber. Conceptually this could be done as simply as by having a spring-loaded door: particles with greater momentum would open the door/gate/valve and others would not. In practice, at normal temperatures the dissipation of energy caused by transfer of energy from the bouncing particles to the side walls, to each other, and of course to the valve in their passage through the wall, would soon cause the whole system to lose energy and run down. Recent research suggests that this might not be the case at super-low temperatures.[1]

Applications

Real-life versions of Maxwellian demons occur, but all such "real demons" have their entropy-lowering effects duly balanced by increase of entropy elsewhere.

Single-atom traps used by particle physicists allow an experimenter to control the state of individual quanta in a way similar to Maxwell's demon.

In living systems the ion channels and pumps are very similar to Maxwell's demon. These biochemical pumps make nervous systems work, including the human brain.

Molecular-sized mechanisms are no longer found only in biology; they are also the subject of the emerging field of nanotechnology.

A large-scale, commercially-available pneumatic device exists which separates hot and cold air, called a Ranque-Hilsch vortex tube. It sorts molecules by exploiting the conservation of angular momentum: hotter molecules are spun to the outside of the tube while cooler molecules spin in a tighter whirl within the tube. Gas from the two different temperature whirls may be vented on opposite ends of the tube. Although this creates a temperature difference, the energy to do so is supplied by the pressure driving the gas through the tube.

If hypothetical mirror matter exists, demons can be envisaged which can act like perpetuum mobiles of the second kind: extract heat energy from only one reservoir, use it to do work and be isolated from the rest of ordinary world. Yet the Second Law is not violated because the demons pay their entropy cost in the hidden (mirror) sector of the world by emitting mirror photons.

Adams and the demon as historical metaphor

Historian Henry Adams in his manuscript The Rule of Phase Applied to History attempted to use Maxwell's demon as an historical metaphor though he seems to have misunderstood and misapplied the principle.[3] Adams interpreted history as a process moving towards equilibrium, but he saw militaristic nations (he felt Germany pre-eminent in this class) as tending to reverse this process, a Maxwell's Demon of history. Adams made many attempts to respond to the criticism of his formulation from his scientific colleagues, but the work remained incomplete at Adams' death in 1918. It was only published posthumously. [4]

See also

Notes

  1. ^ Maxwell (1871), reprinted in Leff & Rex (1990) at p.4
  2. ^ http://www.ulearntoday.com/magazine/physics_article1.jsp?FILE=maxwelldemon
  3. ^ Cater (1947), pp640-647, see also the paper by Daub (1970) reprinted in Leff & Rex (1990), pp37-51.
  4. ^ Adams (1919), p.267
  1. Physical entropy and information entropy
  • Sciencenews.org article about Maxwell's Demon
  • Adams, H. (1919). The Degradation of the Democractic Dogma. New York: Kessinger. ISBN 1-4179-1598-6.
  • Bennet, C.H. (1987) "Demons, Engines and the Second Law", Scientific American, November, pp108-116
  • Cater, H.D (ed.) (1947). Henry Adams and his Friends. Boston. {{cite book}}: |author= has generic name (help); Cite has empty unknown parameter: |1= (help)
  • Daub, E.E. (1967). "Atomism and Thermodynamics". Isis. 58: 293–303.
  • Feynmann, R.P.; et al. (1996). Feynman Lectures on Computation. Addison-Wesley. ISBN 0-14-028451-6. {{cite book}}: Explicit use of et al. in: |author= (help), pp148-150
  • Jordy, W.H. (1952). Henry Adams: Scientific Historian. New Haven. ISBN 0-685-26683-4.
  • Leff, H.S. & Rex, A.F. (eds) (1990). Maxwell's Demon: Entropy, Information, Computing. Bristol: Adam-Hilger. ISBN 0-7503-0057-4. {{cite book}}: |author= has generic name (help)CS1 maint: multiple names: authors list (link), may be out of print but contains several papers not in 2003 edition.
  • - (2003). Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing. Institute of Physics. ISBN 0-7503-0759-5. {{cite book}}: |author= has numeric name (help), Contents - 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.
  • Maxwell, J.C. (1871). Theory of Heat., reprinted (2001) New York: Dover, ISBN 0-486-41735-2
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