Maxwell’s demon

Maxwell's demon
A generic mockup of Maxwell's demon (1871 version), shown in green, who operates a trapdoor between two compartments such as to let the fast moving particles pass from compartment A to B, thus producing a temperature difference without the expenditure of work, thus violating the second law.
In scientific demons, Maxwell’s demon is a hypothetical creature or “very observant and neat-fingered being”, conceived in an 1867 thought experiment by Scottish physicist James Maxwell, 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 cold body to a hot body in contradiction to the second law of thermodynamics.

Letter to Tait | 1867
The creature, as it was originally, was first enunciated by Scottish physicist James Maxwell in a 11 Dec 1867 letter to Scottish physicist Peter Tait, wherein he states: [1]

“To pick a hole–say in the 2nd law of Ωcs, that if two things are in contact the hotter cannot take heat from the colder without external agency.

Now let A & B be two vessels divided by a diaphragm and let them contain elastic molecules in a state of agitation which strike each other and the sides. Let the number of particles be equal in A & B but let those in A have equal velocities, if oblique collisions occur between them their velocities will become unequal & I have shown that there will be velocities of all magnitudes in A and the same in B only the sum of the squares of the velocities is greater in A than in B.

When a molecule is reflected from the fixed diaphragm CD no work is lost or gained.

If the molecule instead of being reflected were allowed to go through a hole in CD no work would be lost or gained, only its energy would be transferred from the one vessel to the other.

Now conceive a finite being who knows the paths and velocities of all the molecules by simple inspection but who can do no work, except to open and close a hole in the diaphragm, by means of a slide without mass.

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.”

Letter to Strutt | 1870
In a 6 Dec 1870 letter to John Strutt, Maxwell states: [16]

“For if there is any truth in the dynamical theory of gases the different molecules in a gas at uniform temperature are moving with very different velocities. Put such a gas into a vessel with two compartments [A and B] and make a small hole in the wall about the right size to let one molecule through. Provide a lid or stopper for this hole and appoint a doorkeeper, very intelligent and exceedingly quick, with microscopic eyes but still an essentially finite being.

Whenever he sees a molecule of great velocity coming against the door from A into B he is to let it through, but if the molecule happens to be going slow he is to keep the door shut. He is also to let slow molecules pass from B to A but not fast ones ... In this way the temperature of B may be raised and that of A lowered without any expenditure of work, but only by the intelligent action of a mere guiding agent (like a pointsman on a railway with perfectly acting switches who should send the express along one line and the goods along another).

I do not see why even intelligence might not be dispensed with and the thing be made self-acting.
Moral The 2nd law of Thermodynamics has the same degree of truth as the statement that if you throw a tumblerful of water into the sea you cannot get the same tumblerful of water out again.”

Theory of Heat | 1871
The demon was detailed in a fuller manner in Maxwell’s famous 1871 book Theory of Heat in a short chapter section entitled “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.”
Left: A 2009 video overview of Maxwell's demon by the Khan Academy. Right: a 2009 "Laplace's demon meets Maxwell's demon" dialog between James Maxwell's 1867 version of a "being" talking to Pierre Laplace's version of a "being" (Laplace's demon).

Thomson's demon namesake | 1874
See main: Scientific demon
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”, who states in a footnote: [10]

“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]

Concerning Demons | 1876
In circa 1876, Maxwell sent a undated note to letter entitled ‘Concerning Demons’ to his associate Scottish physicist Peter Tait, which contains the following: [14]

Concerning Demons
1. Who gave them this name? Thomson.
2. What were they by nature? Very small BUT lively beings incapable of doing work but able to open and shut valves which move without friction or inertia.
3. What was their chief end? To show that the 2nd Law of Thermodynamics has only a statistical certainty.
4. Is the production of an inequality of temperature their only occupation? No, for less intelligent demons can produce a difference while stopping all those going the other way. This reduces the demon to a valve. As such a value him. Call him no more a demon but a valve like that of the hydraulic ram, suppose.

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, in his
“Maxwell’s Demon Cannot Operate: Information and Entropy”, is said to have exorcized Maxwell’s demon by showing that, to operate properly, it need information about the position and velocities of the molecules. Subsequently, in an isolated, isochoric (constant volume) system with a uniform temperature, the demon can only see black body 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 physical 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 thermodynamics, 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]

Literature thermodynamics
Polish writer Stanislaw Lem (1921-2006) employs an information theory type of demon in his 1965 The Cyberiad, as what he calls a “demon of the second kind”, that recognizes when molecules form words, that the demon writes down with a diamond-tipped pen. [13] American writer Thomas Pynchon employs a Maxwell's demon in his novels.

Depictions
The following are a collection of Maxwell demon image depictions:


Szilard demon
Escher house Maxwell demonMaxwell's demon
A 2008 rendition of the Szilard demon (or Szilard’s heat engine), according to which a chamber of volume V contains a one-molecule gas, which can be found in either the right or the left part of the box. (a) Initially, the position of the molecule is unknown. (b) Maxwell’s demon inserts a partition at the center and observes the molecule to determine whether it is in the right or the left hand side of the partition. He records this information in his memory. (c) Depending on the outcome of the measurement (which is recorded in his memory), the demon connects a load to the partition. If the molecule is in the right part as shown in the figure, he connects the load to the right hand side of the partition. (d) The isothermal expansion of the gas does work upon the load, whose amount is kT ln 2. [15]A 2010 Escher house, built of polystyrene beads, with a perpetual motion water wheel being run by a Maxwell’s demon. [12]Hungarian-American physicist Leó Szilárd's 1929 interpretation of Maxwell's demon as an entity (Szilard's demon) that would need a light source to measure the position of each particle.



Maxwell demon (Russian)Maxwell's Demon 2 (cropped cover)Maxwell's demon (cartoon)
A Russian-drawing of a Maxwell demon. [11]Harvey Leff and Andrew Rex's 2002 depiction of James Maxwell and his demon. [6]A Maxwell's demon comic.

Other
In 1967, English physicist Werner Ehrenberg published a ten page essay entitled "Maxwell's Demon". [17]

See also
Laplace’s demon
Szilard’s demon
Louis Filon

References
1. (a) Maxwell, James. (1867). Letter to Peter Guthrie Tait (11 Dec). In P. M. Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 331-2.
(b) 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.
(c) Cápek, Vladislav and Sheehan, Daniel P. (2005). Challenges to the Second Law of Thermodynamics: Theory and Experiment, (pgs. 35-36). Springer.
(d) Thermodynamics quotations – TodayInSci.com.
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).
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. (a) Perrot, Pierre. (1998). A to Z of Thermodynamics, (pgs. 194-95). Oxford: Oxford University Press.
(b) Brillouin, Leon. (1951). “Maxwell’s Demon Cannot Operate: Information and Entropy” (abs), Journal of Applied Physics, 22(3):334-37.
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.
11. The Maxwell Demon (ChipDipVideo) (2011) – YouTube.
12. Cartlidge, Edwin. (2010). “Information Converted to Energy”, PhysicsWorld.com, Nov. 19.
13. (a) Hayles, N. Katherine. (1991). Chaos Bound: Orderly Disorder in Contemporary Literature and Science (pg. 7). Cornell University Press.
(b) Gold, Barri J. (2010). ThermoPoetics: Energy in Victorian Literature and Science (pg. 250). MIT Press.
(c) The Cyberiad – Wikipedia.
14. (a) Ubbelohde, Alfred René. (1954). Man and Energy: Illustrated (pg. 184). Hutchinson's Scientific & Technical Publications.
(b) Earman, John and Norton, John D. (1998). “Exorcist XIV: The Wrath of Maxwell’s Demon. Part I. From Maxwell to Szilard” (abs), Studies in History and Philosophy of Modern Physics, 29(4):435-71.
15. Maruyama, Koki, Nori, Franco, and Vedral, Vlatko. (2009). “The Physics of Maxwell’s Demon and Information” (abs), Reviews of Modern Physics, 81(1):1-23, ArXiv.org preprint, 2008.
16. (a) Maxwell, James. (1870). Letter to John William Strutt (6 Dec). In P. M. Hannan (ed.), The Scientific Letters and Papers of James Clerk Maxwell (1995), Vol. 2, 582-3.
(b) Thermodynamics quotations – TodayInSci.com.
17. Ehrenberg, Werner. (1967). “Maxwell’s Demon” (pdf), Scientific America, 217(5):103-110, Nov.

Further reading
● McClare, C.W.F. (1971). “Chemical Machines, Maxwell’s Demon, and Living Organisms” (abs), Journal of Theoretical Biology, 1(30): 1-34.
● Earman, John and Norton, John D. (1999). “Exorcist XIV: The Wrath of Maxwell’s Demon. Part II. From Szilard to Landauer and Beyond” (abs), Studies in History and Philosophy of Modern Physics, 29(4):435-71.
● Cockshott, Paul and Michaelson, Greg. (2005). “Information, Work, and Meaning”, 105-pgs. University of Glasgow.
● Merali, Zeeya. (2010). “Demonic Device Converts Information to Energy: Experiment Inspirired by a Paradox Tempts a Bead Uphill”, Nature.com, Nov. 14.

External links
Maxwell’s demon – Wikipedia.

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