In thermodynamics, Maxwell’s demon is a hypothetical creature or “very observant and neat-fingered being” that is able to open a frictionless trapdoor between two chambers of gas particles at different temperatures in such a manner that it could intelligently sort the particles by speed, thus moving heat, without the expenditure of work, from a cold body to a hot body in contradiction to the second law of thermodynamics.

The creature, as it was originally called, was conceived by Scottish physicist James Maxwell in an 1867 letter to Scottish physicist Peter Tait [1] In this letter, Maxwell writes: [5]

“Let him [demon] first observe the molecules [in compartment] A and when he sees one coming the square of whose velocity is less than the mean square velocity of the molecules in B let him open the hole and let it go into B. Next let him watch for a molecule of [compartment] B, the square of whose velocity is greater than the mean square velocity in A, and when it comes to the hole let him draw the slide and let it go into A, keeping the slide shut for all other molecules.”

The demon was detailed in a fuller manner in Maxwell’s famous 1871 Theory of Heat in a short section titled “Limitation of the Second Law of Thermodynamics” in which he states that in a system enclosed in an envelope which permits neither volume change nor the passage of heat, in which the temperature and pressure are uniform, it is "impossible to produce any inequality of temperature or pressure without the expenditure of work". This statement, according to Maxwell, is one of the best established facts in thermodynamics and is called the second law of thermodynamics. On this platform, Maxwell lays out the following thought experiment: [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.”

The term demon, to note, was never used by Maxwell. The actual term “demon” was first introduced by British physicist William Thomson in his 1874 article “Kinetic Theory of the Dissipation of Energy”. [10] In particular, Thomson states in a footnote that:

“The definition of a ‘demon’, according to the use of this word by Maxwell, is an intelligent being endowed with free will, and fine enough tactile and perceptive organization to give him the faculty of observing and influencing individual molecules of matter.”

Later, Thomson elaborated on the demon in his 1879 lecture “The Sorting Demon of Maxwell”. [9] In this lecture, in commentary on the demon, Thomson stated that “the conception of the ‘sorting demon’ is purely mechanical … It was not invented to help us deal with questions regarding the influence of life and of mind on the motions of matter.” [3]

Exorcisms
In the decades to follow Maxwell’s thought experiment, it soon became clear that such a creature contradicts the second law. It was a puzzle that needed solution. The first exorcism of the demon came from Polish statistical physicist Marian Smoluchowski who in 1912, in a lecture entitled “Experimentally Verifiable Molecular Phenomena that Contradicts Ordinary Thermodynamics", argued that thermal fluctuations would prevent any automatic device from operating successfully as a Maxwell demon. [7] In other words, because of Brownian movement, the door would heat up and begin to vibrate, from the gas molecules colliding against it, and would cease to work as a one-way valve. [1]

In 1929, Hungarian-American physicist Leó Szilárd devoted his thesis “On the Increase of Entropy in a Thermodynamical System by the Action of Intelligent Beings” to Maxwell’s demon, noting that the demon would require the use of information. [1] In 1951, French physicist Léon Brillouin exorcized Maxwell’s demon by showing that, to operate properly, it need information about the position and velocities of the molecules. [8] Subsequently, in an isolated, isochoric (constant volume) system with a uniform temperature, the demon can only see blackbody radiation and therefore cannot operate its valve. The situation, however, may be altered by letting external radiation penetrate the system, thus allowing the demon to “see” the molecules. Hence, for the demon to operate, it will need an external energy source. Said another way, to get the information needed, according to the second law, the demon will consume more negentropy than it will create by working the valve. [8]

Influence
In 1909, American historian thermodynamic historian Henry Adams used the demon in his manuscript The Rule of Phase Applied to History. Maxwell’s conception of a “sorting demon” also influenced American mathematical child prodigy William James Sidis in the publication of his 1920 The Animate and the Inanimate. [4] In literature, Maxwell’s demon appears in American author Thomas Pynchon’s novels, The Crying of Lot 49 and Gravity's Rainbow.

In computer science thermodynamics, Maxwell's demon is currently a hot topic, particularly in information theory, popularized greatly by the book Maxwell's Demon, having a 1990 first edition and a 2002 second edition titled Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing (shown adjacent), by authors Harvey Leff and Andrew Rex. [6]

References
1. Schmitz, John E.J. (2007). The Second Law of Life: Energy, Technology, and the Future of Earth as We Know It, (pg. 151). William Andrew Publishing.
2. Maxwell, James. (1971). Theory of Heat, (pg. 338). London: Longmans, Green, and Co.
3. Baeyer, Hans C. von (1999). Warmth Disperses and Time Passes - the History of Heat (previously published as Maxwell’s Demon), (ch. 12: “The Mechanical Demon”, pgs. 92-98). New York: The Modern Library.
4. Sidis, William J. (1920). The Animate and the Inanimate, 131-pgs, (published in 1925, R.G. Badger).
5. Cápek, Vladislav and Sheehan, Daniel P. (2005). Challenges to the Second Law of Thermodynamics: Theory and Experiment, (pgs. 35-36). Springer.
6. Leff, Harvey and Rex, Andrew F. (2002). Maxwell’s Demon 2: Entropy, Classical Information, Computing. Taylor & Francis.
7. Zheng, Jianzhou, Zheng, Xiao, Zhao, Yang, Xie, Yang, Yam, ChiYung, Chen, GuanHua, Jiang, Qing, and Chwang Allen T. (2007). “Maxwell’s Demon and Smoluchowski’s Trap Door.” Physical Review E 75, 041109.
8. Perrot, Pierre. (1998). A to Z of Thermodynamics, (pgs. 194-95). Oxford: Oxford University Press.
9. (a) Ilachinski, Andrew. (2001). Cellular Automata: A Discrete Universe, (pg. 310). World scientific.
(b) Kelvin, William Thomson. (1879). “The Sorting Demon of Maxwell”, (pgs. 144-48). Abstract of a Friday Evening Lecture before the Royal Institution of Great Britain, Feb. 28, Proc. R.I. vol. ix. P. 113. (as found in the 1891 book Popular Lectures and Addresses by William Thomson Kelvin, MacMillan and Co.).
10. Thomson, William. (1874). “Kinetic Theory of the Dissipation of Energy” [URL], Nature, April 9, 1874, pg. 441-44.