Maxwell's demon

From Wikipedia, the free encyclopedia

Jump to: navigation, search

Maxwell's demon was an 1867[1] thought experiment by the Scottish physicist James Clerk Maxwell, meant to raise questions about the possibility of violating the second law of thermodynamics.


[edit] Maxwell's thought experiment

The Second Law of Thermodynamics ensures (through statistical improbability) that two bodies of different temperature, when brought into contact with each other and isolated from the rest of the Universe, will evolve to a thermodynamic equilibrium in which both bodies have approximately the same temperature. The second law is also expressed as the assertion that in an isolated system, entropy never decreases.

Maxwell conceived a thought experiment as a challenge to the second law. He described the experiment as follows[2]:

... 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.

Schematic figure of Maxwell's demon

In other words, Maxwell imagines two containers, A and B. The containers are filled with the same gas at equal temperatures and placed next to each other. Observing the molecules on both sides, an imaginary demon guards a trapdoor between the two containers. 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. The average speed of the molecules in B will have increased while in A they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in A and increases in B, contrary to the second law of thermodynamics.

[edit] Criticism and development

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 argument is to show by calculation that any demon must "generate" more entropy segregating the molecules than it could ever eliminate by the method described. That is, it would take more effort to gauge the speed of the molecules and allow them to selectively pass through the opening between A and B than the amount of energy saved by the difference of temperature caused by this.

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. 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.

Note that if the whole universe consisted of the demon and the container, and energy were needed to operate the gate, the only source of energy is letting heat flow from B to A. Now, the quantum of B to A heat flow is a single particle going from B to A. This restores entropy, because on average the single particles going from B to A are more energetic than the ones going from A to B.

The above argument can take another form if the door is modeled as a potential energy barrier. In order to raise the potential, work must be done, and that potential energy cliff should be higher than the kinetic energy of the particle going from A to B. Thus, the quantum of heat flow going from B to A should be more energetic than the incoming particle.

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.

However, John Earman and John Norton have argued that Szilárd and Landauer's explanations of Maxwell's Demon begin by assuming that the second law of thermodynamics cannot be violated, thus rendering their proofs that Maxwell's Demon cannot violate the Second Law circular.

[edit] 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.

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, called a Ranque-Hilsch vortex tube separates hot and cold air. 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, Zurab Silagadze proposes that 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."

In 1962 lectures, to illustrate thermodynamics, physicist Richard Feynman analyzed a putative Maxwell's demon device, a tiny paddlewheel attached to a ratchet, showing why it cannot extract energy from molecular motion of a fluid at equilibrium.[3] This brownian ratchet is a popular teaching tool.

[edit] Experimental work based on Maxwell's Demon

In the 1 February 2007 issue of Nature, David Leigh, a professor at the University of Edinburgh, announced the creation of a nano-device based on this thought experiment. This device is able to drive a chemical system out of equilibrium, but it must be powered by an external source (light in this case) and therefore does not violate thermodynamics.

Previously, other researchers created a ring-shaped molecule which could be placed on an axle connecting two sites (called A and B). Particles from either site would bump into the ring and move it from end to end. If a large collection of these devices were placed in a system, half of the devices had the ring at site A and half at B at any given moment in time.

Leigh made a minor change to the axle so that if a light is shone on the device, the center of the axle will thicken, thus restricting the motion of the ring. It only keeps the ring from moving, however, if it is at site A. Over time, therefore, the rings will be bumped from site B to site A and get stuck there, creating an imbalance in the system. In his experiments, Leigh was able to take a pot of "billions of these devices" from 50:50 equilibrium to a 70:30 imbalance within a few minutes.[4]

[edit] Adams and the demon as historical metaphor

Historian Henry Brooks Adams in his manuscript The Rule of Phase Applied to History attempted to use Maxwell's demon as a historical metaphor, though he misunderstood and misapplied the original principle.[5] 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.[6]

[edit] Maxwell's demon in popular culture

In literature, Maxwell’s Demon appears in Thomas Pynchon's novels, The Crying of Lot 49 and Gravity's Rainbow. and in George Gamow's Mr. Tompkins. Also, it 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". In Greg Egan's hard science fiction novel Permutation City, Maxwell's Demon is the name of a program used by the character Maria to keep track of individual "molecules" in the cellular automaton known as the Autoverse. Finally, Maxwell's Demon appears, and fills his typical role, in the climax of the book Master of the Five Magics by Lyndon Hardy. Maxwell's Demon was also mentioned in Christopher Stasheff's books from the series A Wizard in Rhyme, wherein he let Maxwell's Demon (Max for short) help out the main character. In Arkady and Boris Strugatsky's book Monday Begins on Saturday two of Maxwell's demons work as doormen in the Institute for Magic and Thaumaturgy.

In the way of short stories, an homage to Maxwell has been written by Isaac Asimov and Larry Niven[citation needed]. Additionally, Larry Niven's Warlock in The Magic Goes Away uses such a demon to cool his home in a vignette titled "Unfinished Story #1" as published in Playgrounds of the Mind (and, earlier, in All the Myriad Ways). The Demon also contributes to the thesis of Ken Kesey's collection of stories, The Demon Box. In the story "A Feast of Demons" by William Morrison (pseudonym for Joseph Samachson), a scientist creates Maxwell's Demons to change the temperature of items, the purity of ores, and eventually even reverse or accelerate the aging process in people--only to have the Demons escape and wreak havoc on civilization. An implementation of a scientifically plausible nanotech version of Maxwell's demon appears in Paul Di Filippo's short story Any Major Dude, the use of which gives a country in the story the name "Maxwell's Land" and its inhabitants "demons."

In music and film, 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, and Maxwell's Demon is the name of a 1968 film by the American experimental filmmaker Hollis Frampton. Maxwell's Demon is mentioned in the song 'A Metaphysical Drama', by Vintersorg and also is the name of a Brooklyn-based indie rock band, as well as that of a London alt-pop band. See also the lyrics to "Isaac's Law" by The Loud Family. Maxwell's Demon is also a song of the electronic music project Adultnapper.

The computer game Maxwell's Maniac on Microsoft Entertainment Pack is loosely based on Maxwell's Demon.

The theory is also referenced in 2003 video-game Max Payne 2, in the form of an in-game cartoon show the chief villain of which is named 'Maxwell's Demon,' a creature said to have been created by 'Doctor Enthropy' and with the goal of turning the world into a 'dreaded closed system.' Also, in the 2007 computer game Neverwinter Nights 2: Mask of the Betrayer the player encounters a puzzle in which he or she controls a trapdoor between two cages containing a mixed population of elemental creatures of fire and ice (mephits, which roughly resemble the classical image of the "demon"), the point of the puzzle being to separate them despite their tendency to mingle, in essence putting the player in the role of Maxwell's Demon.

Citing Maxwell's Demon, math intellectuals philosophized about the actions of an escaped criminal in the American television program Numb3rs. The episode, titled "Arrow of Time", was episode 11 of season 5, and originally aired on January 9, 2009.[7]

A Mac Hall comic depicts the character Matt hallucinating a demon named Maxwell who lives in the air conditioner replacing hot air molecules with cool ones. He claims to refute the Second Law of Thermodynamics.[8]

[edit] See also

[edit] Notes

  1. ^ Concept of the 'demon' first appeared in a letter by Maxwell from 1867, it was mentioned again in a letter from 1870 and presented to the public in his thermodynamics book (Theory of Heat) from 1871. See book Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing by Harvey S. Leff and Andrew F. Rex, CRC Press, 2002, ISBN 0750307595, page 370. Google books link: [1].
  2. ^ Maxwell (1871), reprinted in Leff & Rex (1990) at p.4
  3. ^ Feynman, Richard P. (1963). The Feynman Lectures on Physics, Vol. 1. Massachusetts, USA: Addison-Wesley. Chapter 46. ISBN 0201021161. 
  4. ^ Sanderson, Kathrine (2007-01-31). "A demon of a device". Retrieved on 2007-02-01. 
  5. ^ Cater (1947), pp640-647, see also the paper by Daub (1970) reprinted in Leff & Rex (1990), pp37-51.
  6. ^ Adams (1919), p.267
  7. ^
  8. ^

[edit] References

  • Cater, H.D (ed.) (1947). Henry Adams and his Friends. Boston. 
  • Daub, E.E. (1967). "Atomism and Thermodynamics". Isis 58: 293–303. doi:10.1086/350264. 
  • Leff, H.S. & Rex, A.F. (eds) (1990). Maxwell's Demon: Entropy, Information, Computing. Bristol: Adam-Hilger. ISBN 0-7503-0057-4. 

[edit] Further reading

Personal tools