Maxwell's demon
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.
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
[Maxwell (1871), reprinted in Leff & Rex (1990) at p.4]:
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.
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.
[http://www.ulearntoday.com/magazine/physics_article1.jsp?FILE=maxwelldemon]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]
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.
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.
[Cater (1947), pp640-647, see also the paper by Daub (1970) reprinted in Leff & Rex (1990), pp37-51.] 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.
[Adams (1919), p.267]* Maxwell's demon appears in
George Gamow's
Mr. Tompkins.
* Maxwell's demon is a significant contributing character in
Diane Duane's
Young Wizards Series, primarily in the first book,
So You Want to Be a Wizard.
* Maxwell's demon makes appearances in the popular
manga Oh My Goddess! by
Kosuke Fujishima.
* It also makes appearances in
Her Majesty's Wizard by
Christopher Stasheff.
* Maxwell's demon is mentioned in the Novel
Homo Faber by
Swiss author
Max Frisch, as well as in one of the short stories of
The Cyberiad by
Stanisław Lem: "The Sixth Sally, or How Trurl and Klaupacius Created a Demon of the Second Kind to Defeat the Pirate Pugg".
*
Isaac Asimov and
Larry Niven have also each written a short story in homage to Maxwell. Additionally,
Larry Niven's Warlock in
The Magic Goes Away uses such a demon to cool his home.
* Some Windows releases came with a very simple game called "
Maxwell's Maniac", in which you play the part of Maxwell's Demon by moving a sliding door to try to coax red molecules to one side of a chamber and blue molecules to the other.
*Maxwell's Demon becomes an argument for
The User Illusion by
Tor Norretranders.
*Maxwell Demon was the name of
Brian Eno's first band, which was the inspiration for the name of a fictional character in the movie
Velvet Goldmine.Maxwell's Demon is the name of a 1968 film by the American experimental filmmaker
Hollis Frampton.
Maxwell's Demon is an enemy of Captain Baseball bat-boy in the animated series featured in the game
Max Payne.
*In strip 346 of the webcomic
Mac Hall, a hallucinated Maxwell's Demon is found in the air conditioner.
*
Evaporation*
Thermionic emission*
Photoelectric effect*
Joule-Thompson effect*
Hall effect*
Mass spectrometry*
Dispersion*
Catalysis*
Quantum tunneling*
Gibbs paradox#
Physical entropy and information entropy*
Sciencenews.org article about Maxwell's Demon* Bennet, C.H. (1987) "Demons, Engines and the Second Law",
Scientific American, November,
pp108-116
*
* ,
pp148-150
* , may be out of print but contains several papers not in 2003 edition.
* ,
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.
* , reprinted (2001) New York: Dover, ISBN 0486417352
