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Maxwell's demon

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In the philosophy of thermal and statistical physics, Maxwell's demon is a thought experiment created by the physicist James Clerk Maxwell to "show that the Second Law of Thermodynamics has only a statistical certainty".[1] It demonstrates Maxwell's point by hypothetically describing how to violate the Second Law: a container is divided into two parts by an insulated wall, with a door that can be opened and closed by what came to be called "Maxwell's demon". The demon opens the door to allow only the "hot" molecules of gas to flow through to a favoured side of the chamber, causing that side to gradually heat up while the other side cools down, thus decreasing entropy.

Origin and history of the idea

The thought experiment first appeared in a letter Maxwell wrote to Peter Guthrie Tait on 11 December 1867. It appeared again in a letter to John William Strutt in 1870, before it was presented to the public in Maxwell's 1871 book on thermodynamics titled Theory of Heat.[2]

In his letters and book, Maxwell described the agent opening the door between the chambers as a "finite being". William Thomson (Lord Kelvin) was the first to use the word "demon" for Maxwell's concept, in the journal Nature in 1874, and implied that he intended the mediating, rather than malevolent, connotation of the word.[3][4][5]

Original thought experiment

The second law of thermodynamics ensures (through statistical probability) 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 way of furthering the understanding of the second law. His description of the experiment is as follows:[6]

... 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 one container divided into two parts, A and B. Both parts 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 parts. 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. Likewise, when a slower-than-average molecule from B flies towards the trapdoor, the demon will let it pass from B to A. 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.

Note that the demon must allow molecules to pass in both directions in order to produce only a temperature difference; one-way passage only of faster-than-average molecules from A to B will cause higher temperature and pressure to develop on the B side. In fact, because temperature and pressure are related, if A and B both contain the same numbers of molecule per unit volume, the one with the higher temperature will also have higher pressure; the demon must actually let more slow molecules pass from B to A than fast ones pass from A to B in order to make B hotter at the same pressure. Indeed, by regulating the number of molecules passed in each direction, the demon could achieve a pressure difference instead of a temperature difference, or any combination of temperature and pressure differences (possibly including lower pressure on the higher temperature side, depending on the variance in the speeds of the molecules).

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 energy 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. 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.

In 1960, Rolf Landauer raised an exception to this argument. He realized that some measuring processes need not increase thermodynamic entropy as long as they were thermodynamically reversible. He suggested these "reversible" measurements could be used to sort the molecules, violating the Second Law. However, 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 whether to let a molecule through, the demon must acquire information about the state of the molecule and either discard it or store it. Discarding it leads to immediate increase in entropy but the demon cannot store it indefinitely: In 1982, 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. Although Bennett had reached the same conclusion as Szilard’s 1929 paper, that a Maxwellian demon could not violate the second law because entropy would be created, he had reached it for different reasons.

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 by the demon, and derive further properties of the demon from this assumption, including the necessity of consuming energy when erasing information, etc. It would therefore be circular to invoke these derived properties to defend the second law from the demonic argument. Bennett later acknowledged the validity of Earman and Norton's argument, while maintaining that Landauer's principle explains the mechanism by which real systems do not violate the second law of thermodynamics.[7]

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.[8] This Brownian ratchet is a popular teaching tool.

Experimental work

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.[9]

The March 2011 issue of Scientific American features an article by Professor Mark G. Raizen of the University of Texas, Austin which discusses the first realization of Maxwell's demon with gas phase particles, as originally envisioned by Maxwell. In 2005, Raizen and collaborators showed how to realize Maxwell's demon for an ensemble of dilute gas-phase atoms or molecules. The new concept is a one-way wall for atoms or molecules that allows them move in one direction, but not go back. The operation of the one-way wall relies on an irreversible atomic and molecular process of absorption of a photon at a specific wavelength, followed by spontaneous emission to a different internal state. The irreversible process is coupled to a conservative force created by magnetic fields and/or light. Raizen and collaborators proposed to use the one-way wall in order to reduce the entropy of an ensemble of atoms. In parallel, Gonzalo Muga and Andreas Ruschhaupt, independently developed a similar concept. Their "atom diode" was not proposed for cooling, but rather to regulate flow of atoms. The Raizen Group demonstrated significant cooling of atoms with the one-way wall in a series of experiments in 2008. Subsequently, the operation of a one-way wall for atoms was demonstrated by Daniel Steck and collaborators later in 2008. Their experiment was based on the 2005 scheme for the one-way wall, and was not used for cooling. The cooling method realized by the Raizen Group was called "Single-Photon Cooling," because only one photon on average is required in order to bring an atom to near-rest. This is in contrast to laser cooling which uses the momentum of the photon and requires a two-level cycling transition.

In 2006 Raizen, Muga, and Ruschhaupt showed in a theoretical paper that as each atom crosses the one-way wall, it scatters one photon, and information is provided about the turning point and hence the energy of that particle. The entropy increase of the radiation field scattered from a directional laser into a random direction is exactly balanced by the entropy reduction of the atoms as they are trapped with the one-way wall. Therefore, single-photon cooling is a physical realization of Maxwell’s Demon in the same sense envisioned by Leo Szilard in 1929.

The importance of single photon cooling is that it provides a general method for cooling multi-level atoms or molecules. It circumvents the limitation of laser cooling which requires a two-level cycling transition, and hence is limited to a small set of atoms in the Periodic Table. The experimental realization of Maxwell's demon is a key step towards general control of atoms in gas phase. Beyond basic scientific research, these methods will enable efficient isotope separation for medicine and basic research, as well as controlling atoms in gas phase for nanoscale deposition on surfaces. This new, bottom-up, approach to nanoscience is called Atomoscience and is enabled by the realization of Maxwell's demon.

Regarding Landauer's principle, the minimum energy dissipated by deleting information was experimentally measured by Eric Lutz et al. in 2012.[10] Although a demon could, in principle, observe the particle, save the result and act on it, deleting the result would necessarily dissipate heat and thus increase entropy. Without an infinite memory, the demon would eventually have to overwrite its previous results. Additionally, the deletion became more energy-efficient the slower it was, thus also requiring the demon to asymptotically approach zero processing speed.

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.[11] 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.[12]

See also

Notes

  1. ^ Cargill Gilston Knott (1911). "Quote from undated letter from Maxwell to Tait". Life and Scientific Work of Peter Guthrie Tait. Cambridge University Press. p. 215.
  2. ^ Leff & Rex (2002), p. 370.
  3. ^ William Thomson (1874). "Kinetic theory of the dissipation of energy". Nature. 9 (232): 441–444. Bibcode:1874Natur...9..441T. doi:10.1038/009441c0.{{cite journal}}: CS1 maint: numeric names: authors list (link)
  4. ^ "The sorting demon Of Maxwell". Proceedings of the Royal Institution. ix: 113. 1879.
  5. ^ Alan S. Weber (2000). Nineteenth Century Science: a Selection of Original Texts. Broadview Press. p. 300.
  6. ^ Maxwell (1871), reprinted in Leff & Rex (1990) on p. 4.
  7. ^ Charles H. Bennett (2002–2003). "Notes on Landauer's principle, reversible computation, and Maxwell's demon" (PDF). arXiv:physics/0210005. {{cite journal}}: Cite journal requires |journal= (help)
  8. ^ Feynman, Richard P. (1963). The Feynman Lectures on Physics, Vol. 1. Massachusetts, USA: Addison-Wesley. Chapter 46. ISBN 0-201-02116-1. {{cite book}}: Unknown parameter |nopp= ignored (|no-pp= suggested) (help)
  9. ^ Katharine Sanderson (31 January 2007). "A demon of a device". Nature. doi:10.1038/news070129-10. {{cite news}}: |access-date= requires |url= (help)
  10. ^ http://www.nature.com/news/the-unavoidable-cost-of-computation-revealed-1.10186
  11. ^ Cater (1947), pp. 640–647; see also Daub (1970), reprinted in Leff & Rex (1990), pp. 37–51.
  12. ^ Adams (1919), p. 267.

References

  • Cater, H. D., ed. (1947). Henry Adams and his Friends. Boston.
  • Daub, E. E. (1967). "Atomism and Thermodynamics". Isis. 58 (3): 293–303. doi:10.1086/350264.
  • Leff, Harvey S. & Andrew F. Rex, ed. (1990). Maxwell's Demon: Entropy, Information, Computing. Bristol: Adam-Hilger. ISBN 0-7503-0057-4.
  • Leff, Harvey S. & Andrew F. Rex, ed. (2002). Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing. CRC Press. ISBN 0-7503-0759-5.
  • Adams, H. (1919). The Degradation of the Democractic Dogma. New York: Kessinger. ISBN 1-4179-1598-6.
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