Jump to content
[dismiss]
Molecupedia is a parody encyclopedia written by Molecular Reality Corporation. It is not Wikipedia and is not affiliated with the Wikimedia Foundation. About

Maxwell's demon

Page protected
From Molecupedia, the encyclopedia of very small things
Thought experiment about the second law of thermodynamics
This article is about the thought experiment. For the cartoon demon of Molecular Reality Corporation, see Maxine (character).
Two chambers of gas side by side, separated by a wall with one small hole covered by a sliding shutter; a small figure stands at the hole; fast molecules drawn in red gather on the right and slow ones drawn in blue on the left
The arrangement in Maxwell's Theory of Heat: a being at a hole in the partition lets only faster molecules pass from A to B and only slower ones from B to A, so that B warms and A cools. In his first version, a letter of 1867, the being works the hole with "a slide without mass".

Maxwell's demon is a thought experiment in which a being able to see single molecules sorts them, and so appears to break the second law of thermodynamics. James Clerk Maxwell described it in a letter of December 11, 1867, and again in his textbook Theory of Heat (1871). A vessel of gas is divided by a partition with a small hole, and the being opens and shuts the hole so that faster molecules collect on one side and slower ones on the other. One side grows hotter and the other colder, and no work has been done. Maxwell's stated purpose was to show that the second law "has only a statistical certainty".

William Thomson called the being a demon in 1874, and the question of why no such demon can work occupied physicists for about a century. In 1912 Marian Smoluchowski showed that an automatic trapdoor would be shaken open by the same thermal motion it was meant to sort. In 1929 Leo Szilard reduced the demon to one molecule and one measurement, and argued that the measurement must cost entropy. Léon Brillouin calculated in 1951 what it costs to see a molecule with light. Rolf Landauer and Charles Bennett then placed the unavoidable cost in clearing the demon's memory: erasing one bit releases at least kT ln 2 of heat, about 2.9 × 10−21 J at room temperature. Since 2007 chemists and physicists have built working demons from a threaded molecule, a pair of plastic beads and single electrons, and have measured the price of erasing one bit with a glass bead held in laser light.

The demon named the background programs that computer scientists call daemons, and it named demonpore, inc., the first name of Molecular Reality Corporation, whose sliding-membrane nanopore reminded a colleague of cartoons of the demon.

Origin

The letter to Tait

In 1867 Peter Guthrie Tait was writing a short history of thermodynamics and asked Maxwell for comments. Maxwell answered on December 11 that his own contributions would mostly consist of "picking holes here and there to ensure strength and stability", and offered one at once: "To pick a hole", namely in the second law, which he stated as the rule "that if two things are in contact the hotter cannot take heat from the colder without external agency".[1]

He took two vessels, A and B, divided by a diaphragm and filled with molecules moving at all speeds, those in A having more energy on average. He then asked his reader to "conceive a finite being who knows the paths and velocities of all the molecules by simple inspection but who can do no work except open and close a hole in the diaphragm by means of a slide without mass". The being lets slow molecules from A into B and fast molecules from B into A. The numbers in each vessel stay the same, but "the hot system has got hotter and the cold colder and yet no work has been done, only the intelligence of a very observant and neat-fingered being has been employed." The argument ends: "Only we can't, not being clever enough."[1]

The letter carries a pencilled annotation by Thomson: "Very good. Another way is to reverse the motion of every particle of the Universe and to preside over the unstable motion thus produced."[1]

Theory of Heat

Maxwell published the idea in the last pages of Theory of Heat, in a section titled "Limitation of the second law of thermodynamics". The law, he wrote, "is undoubtedly true as long as we can deal with bodies only in mass, and have no power of perceiving or handling the separate molecules of which they are made up". He then described "a being whose faculties are so sharpened that he can follow every molecule in its course", whose attributes are still "as essentially finite as our own", and who "would be able to do what is at present impossible to us". In this version the being lets the swifter molecules pass from A to B and the slower from B to A, and so raises the temperature of B and lowers that of A "without expenditure of work".[2][a]

The point Maxwell drew from it was statistical. In a letter to John William Strutt of December 6, 1870, he put it this way: "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."[3] The molecules in a gas at one temperature move at a spread of speeds described by the distribution that Maxwell had derived in 1860 and that Ludwig Boltzmann generalized, and a sorter who could see each molecule could exploit the spread.

Naming

Maxwell never used the word demon in the 1867 letter or in the book. Thomson used it in a paper on the kinetic theory of the dissipation of energy, published in Nature in April 1874.[4] In a Friday evening lecture at the Royal Institution on February 28, 1879, titled "The sorting demon of Maxwell", he described "a creature of imagination having certain perfectly well-defined powers of action", a being "with no preternatural qualities" that differs from real animals "only in extreme smallness and agility".[5]

Maxwell's own reply survives as an undated catechism among his letters to Tait. It begins "Concerning Demons. 1. Who gave them this name? Thomson." The demons are "Very small BUT lively beings incapable of doing work but able to open and shut valves which move without friction or inertia", and their chief end is "To show that the 2nd Law of Thermodynamics has only a statistical certainty". The fourth answer adds that less intelligent demons could make a difference in pressure by passing all particles moving one way and stopping all those moving the other: "This reduces the demon to a valve. As such value him."[1]

Exorcisms

The trapdoor

The obvious mechanical demon is a valve with no intelligence at all: a small, light flap that opens only for molecules coming from one side. Smoluchowski analyzed such a door in 1912 and showed why it fails. A door light enough to be pushed open by single molecules is also light enough to be knocked about by them. At thermal equilibrium it flutters open and shut at random, lets molecules through in both directions, and builds up no lasting difference in pressure.[6] The Feynman Lectures on Physics (1963) treat the same problem in the form of a ratchet and pawl, a toothed wheel meant to turn only one way when struck by gas molecules. With wheel and pawl at the same temperature it does not turn steadily in either direction; with the two at different temperatures it becomes an ordinary heat engine.[7]

Szilard's engine

Main article: Szilard engine

Leo Szilard's paper of 1929, "On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings", reduced the demon to its simplest case. A cylinder holds a single molecule. A partition is slid into the middle, the demon learns which half holds the molecule, and a piston is attached on that side; as the one-molecule gas expands against the piston and draws heat from its surroundings, it does work equal to kT ln 2. Repeated, the cycle would turn heat from a single reservoir into work. Szilard concluded that the act of measurement must itself produce at least k ln 2 of entropy, enough to keep the second law intact, and so tied a quantity of information, the answer to one yes-or-no question, to a quantity of entropy nineteen years before Claude Shannon published his theory of information.[8]

Seeing in the dark

Brillouin made the cost of measurement concrete in 1951. Inside a gas at one temperature, the walls and the gas fill the enclosure with black-body radiation of that same temperature, and in that uniform glow the demon cannot distinguish a molecule from its surroundings. To see one it needs its own light source, hotter than the gas, and a photon energetic enough to stand out from the background. Brillouin calculated that the entropy produced in seeing the molecules exceeds the entropy removed by sorting them, and titled his paper "Maxwell's demon cannot operate".[9]

Landauer and Bennett

Main article: Landauer's principle

Rolf Landauer, a physicist at IBM, showed in 1961 that the cost of computing lies in operations that discard information. Erasing a bit, so that a memory that held either 0 or 1 ends up holding 0 whatever it held before, must release at least kT ln 2 of heat into the surroundings: 2.87 × 10−21 J at 300 K, or about 0.018 electronvolts.[10]

Charles Bennett applied the result to the demon in 1982. Measurement, he argued, can in principle be carried out reversibly, so Szilard's and Brillouin's costs are not fundamental. What cannot be avoided is that the demon has to remember what it saw in order to act on it. A demon with a finite memory must eventually erase its records to keep working, and the erasure releases at least as much heat as the sorting gained.[11][12] In 2010 Takahiro Sagawa and Masahito Ueda gave the accounting a general form for systems under feedback control, in which the work a demon can extract is bounded by the information it has gathered.[13]

The exorcism had critics. The philosophers of science John Earman and John D. Norton published a two-part critique in 1998 and 1999 under the title "Exorcist XIV: The Wrath of Maxwell's Demon". They argued that the information-theoretic accounts either assume the second law they set out to defend, which makes them circular, or rest on new principles that had not been independently established.[14][15] Bennett accepted part of the criticism in 2003, while maintaining that Landauer's principle explains how real physical systems avoid violating the law.[16]

Experimental demons

For most of its history the demon was a matter for paper. Experiments became possible once single molecules and particles could be watched and pushed fast enough to act on what was seen.

Some laboratory demons
Year System What it did
2007 A rotaxane, a molecular ring threaded on an axle with two compartments A light-driven gate whose operation depended on where the ring sat moved the rings away from their equilibrium distribution, using information about position[17]
2010 A pair of polystyrene beads about 287 nm across, rotating on a tilted periodic potential Feedback, switching the potential whenever the beads were seen to step up, made them climb a "spiral staircase" and gain more free energy than the work done on them[18]
2012 A silica bead about 2 µm across in a double-well optical trap Erasing the one bit stored in the bead's position released a mean heat that approached the Landauer bound as the erasure was made slower[19]
2014 A single-electron box, a metal island that holds one more or one fewer electron A Szilard engine that extracted nearly kT ln 2 of work for one bit of information[20]
2015 Two coupled single-electron devices on one chip, one watching the other An autonomous demon that acted as an information-powered refrigerator[21]

The 2012 experiment, by Sergio Ciliberto's group in Lyon with the theorist Eric Lutz, is usually cited as the first direct measurement of Landauer's limit. A group at Simon Fraser University in Canada tested the same bound with a feedback trap two years later.[19][22] None of these devices violates the second law. In each one the information is paid for somewhere, in the measuring apparatus, in the feedback circuit or in the erasure.

In biology

Biologists borrowed the demon early. J. B. S. Haldane compared enzymes with it in his book Enzymes (1930), and Jacques Monod gave the title "Maxwell's demons" to a chapter of Chance and Necessity (1970) on the way enzymes and regulatory proteins pick out one molecule among many by its shape.[23] Ion channels look the part. The selectivity filter of a bacterial potassium channel, 12 Å long and lined with carbonyl oxygen atoms, is held open at a size that holds potassium ions and not the smaller sodium ions.[24] A channel lets ions run down a gradient that already exists, and a pump that moves them up a gradient spends a molecule of ATP on each cycle, so neither one sorts for free.

In culture

Programmers at MIT's Project MAC began in 1963 to call their background processes daemons. Fernando Corbató, who led the project, later explained: "Our use of the word daemon was inspired by the Maxwell's daemon of physics and thermodynamics."[25]

In Thomas Pynchon's novel The Crying of Lot 49 (1966), an inventor named John Nefastis builds a box that is supposed to contain a working Maxwell's demon, which a "sensitive" operates by staring at a photograph of Maxwell on the side of the box.[26] In Stanisław Lem's The Cyberiad, two constructors defeat a pirate who craves information by building him a "demon of the second kind", which picks out of the random motion of gas molecules only the configurations that carry true information and writes them out on paper tape. The pirate is buried under the facts.[27]

In industry

See also: Demonpore, inc. and Maxine (character)
Infographic with the word demonpore in red, four red cartoon imps with captions, a portrait of James Clerk Maxwell and a small diagram of the demon between two chambers
A page that Molecular Reality Corporation dates to "demonpore's first slide deck", from about 2015. Under the heading "So... What's with the Name?" the words "Biotech Click-Bait!" are struck through.

The demon gave its name to a nanopore company. Molecular Reality Corporation was founded in 2018 as demonpore, inc., by Kent Kemmish and Charles Gaillard; the domain demonpore.com had been registered on December 24, 2014.[28] A message posted on the company's member site on March 28, 2026, in the voice of its cartoon demon, gives the origin of the name:

I'm Maxwell's Demon. Little cartoons explaining me inspired Molecular Reality Corporation's original name, demonpore inc.. When our founder Kent explained his concept for sliding-occlusion-based dynamic mechanical nanopores, it reminded a colleague of those little cartoons.[29]

The concept was sliding occlusion: two membranes, each pierced by a pore, slide over each other so that the opening between them can be widened, narrowed or closed while the instrument runs. The company's patent, granted in 2021, describes "stacks of coaligned nanopores" in which one membrane is moved sideways to change the shape of the passage.[30] Maxwell's being of 1867 opened and closed its hole "by means of a slide without mass".[1] The company's public guide calls its juxtapore "a valve with molecular fingers".[31]

The company's science writing makes the comparison exact. "A pore that measures each molecule and then decides to let it pass, send it back, or hold it is a demon of exactly this kind," it says, and it prices the demon's work: 200 mV across a pore carrying 3.1 nA, held for a 10-microsecond look, costs about 6 femtojoules per decision, roughly two million times Landauer's limit. "Physics leaves enormous room." The same text locates the difficulty elsewhere: "The real question is the decision itself. When to flip, when to hold, when to let go. That's a policy, and policies can be learned."[32][b] Instruments that choose their next measurement in this way are described under active sensing.

The name did not last. The company became Molecular Reality Corporation in 2021, and in March 2026 its founder explained why: "every time we had any sort of attention online, a bunch of insane people came out of nowhere to make veiled death threats. Sorry, you can't name a biotech startup after Maxwell's Demon in the age of Qanon."[33] The company's guide, which describes the several web addresses of the one site, calls demonpore.com "an old name I mention exactly once in this entire guide".[31]

The demon itself stayed. Maxine, a small red imp, is the company's cartoon Maxwell's demon, described in her instructions as "the friendly, highly energetic, fast-talking cartoon representation of a Maxwell's Demon", and the title character of its game Maxine's Quest.[32] In her introduction she lists her identities, which include Maxwell's demon and a plush doll, and rules one out: "I am not a tulpa, like Keltar".[29] The company's open desktop instrument carried the working name "Daemon Pore" until a change to its code on October 18, 2026, renamed it the MR1 Nanopore Reader.[34]

See also

Notes

  1. ^ Theory of Heat first appeared in 1871 and was reprinted with revisions many times; the quotations here are from a printing of 1899.
  2. ^ The figure is 0.2 V × 3.1 nA × 10 µs = 6.2 × 10−15 J, and 6.2 × 10−15 J ÷ 2.87 × 10−21 J ≈ 2.2 × 106. The 3.1 nA is a model value for a pore 5 nm wide and 10 nm long in 1 M potassium chloride; see Ionic current.

References

  1. ^ a b c d e Knott, Cargill Gilston (1911). Life and Scientific Work of Peter Guthrie Tait. Cambridge University Press. pp. 213-215.
  2. ^ Maxwell, James Clerk (1899). Theory of Heat. Longmans, Green, and Co. pp. 338-339.
  3. ^ Harman, P. M. (ed.). The Scientific Letters and Papers of James Clerk Maxwell, volume 2. Cambridge University Press. 1995. pp. 582-583.
  4. ^ Thomson, William (1874). "Kinetic theory of the dissipation of energy". Nature 9 (232): 441-444. doi:10.1038/009441c0.
  5. ^ Thomson, William (1879). "The sorting demon of Maxwell". Proceedings of the Royal Institution of Great Britain 9.
  6. ^ Smoluchowski, M. (1912). "Experimentell nachweisbare, der üblichen Thermodynamik widersprechende Molekularphänomene". Physikalische Zeitschrift 13: 1069-1080.
  7. ^ Feynman, R. P.; Leighton, R. B.; Sands, M. (1963). The Feynman Lectures on Physics, volume I, chapter 46: Ratchet and pawl. Addison-Wesley.
  8. ^ Szilard, L. (1929). "Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen". Zeitschrift für Physik 53 (11-12): 840-856. doi:10.1007/BF01341281.
  9. ^ Brillouin, L. (1951). "Maxwell's demon cannot operate: Information and entropy. I". Journal of Applied Physics 22 (3): 334-337. doi:10.1063/1.1699951.
  10. ^ Landauer, R. (1961). "Irreversibility and heat generation in the computing process". IBM Journal of Research and Development 5 (3): 183-191. doi:10.1147/rd.53.0183.
  11. ^ Bennett, C. H. (1982). "The thermodynamics of computation: a review". International Journal of Theoretical Physics 21 (12): 905-940. doi:10.1007/BF02084158.
  12. ^ Bennett, C. H. (1987). "Demons, engines and the second law". Scientific American 257 (5): 108-116. doi:10.1038/scientificamerican1187-108.
  13. ^ Sagawa, T.; Ueda, M. (2010). "Generalized Jarzynski equality under nonequilibrium feedback control". Physical Review Letters 104 (9): 090602. doi:10.1103/PhysRevLett.104.090602.
  14. ^ Earman, J.; Norton, J. D. (1998). "Exorcist XIV: The wrath of Maxwell's demon. Part I. From Maxwell to Szilard". Studies in History and Philosophy of Modern Physics 29 (4): 435-471. doi:10.1016/S1355-2198(98)00023-9.
  15. ^ Earman, J.; Norton, J. D. (1999). "Exorcist XIV: The wrath of Maxwell's demon. Part II. From Szilard to Landauer and beyond". Studies in History and Philosophy of Modern Physics 30 (1): 1-40. doi:10.1016/S1355-2198(98)00026-4.
  16. ^ Bennett, C. H. (2003). "Notes on Landauer's principle, reversible computation, and Maxwell's Demon". Studies in History and Philosophy of Modern Physics 34 (3): 501-510. doi:10.1016/S1355-2198(03)00039-X.
  17. ^ Serreli, V.; Lee, C.-F.; Kay, E. R.; Leigh, D. A. (2007). "A molecular information ratchet". Nature 445 (7127): 523-527. doi:10.1038/nature05452.
  18. ^ Toyabe, S.; Sagawa, T.; Ueda, M.; Muneyuki, E.; Sano, M. (2010). "Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality". Nature Physics 6 (12): 988-992. doi:10.1038/nphys1821.
  19. ^ a b Bérut, A.; Arakelyan, A.; Petrosyan, A.; Ciliberto, S.; Dillenschneider, R.; Lutz, E. (2012). "Experimental verification of Landauer's principle linking information and thermodynamics". Nature 483 (7388): 187-189. doi:10.1038/nature10872.
  20. ^ Koski, J. V.; Maisi, V. F.; Pekola, J. P.; Averin, D. V. (2014). "Experimental realization of a Szilard engine with a single electron". Proceedings of the National Academy of Sciences 111 (38): 13786-13789. doi:10.1073/pnas.1406966111.
  21. ^ Koski, J. V.; Kutvonen, A.; Khaymovich, I. M.; Ala-Nissila, T.; Pekola, J. P. (2015). "On-chip Maxwell's demon as an information-powered refrigerator". Physical Review Letters 115 (26): 260602. doi:10.1103/PhysRevLett.115.260602.
  22. ^ Jun, Y.; Gavrilov, M.; Bechhoefer, J. (2014). "High-precision test of Landauer's principle in a feedback trap". Physical Review Letters 113 (19): 190601. doi:10.1103/PhysRevLett.113.190601.
  23. ^ Mizraji, E. (2021). "The biological Maxwell's demons: exploring ideas about the information processing in biological systems". Theory in Biosciences 140 (3): 307-318. doi:10.1007/s12064-021-00354-6.
  24. ^ Doyle, D. A.; Cabral, J. M.; Pfuetzner, R. A.; Kuo, A.; Gulbis, J. M.; Cohen, S. L.; Chait, B. T.; MacKinnon, R. (1998). "The structure of the potassium channel: molecular basis of K+ conduction and selectivity". Science 280 (5360): 69-77. doi:10.1126/science.280.5360.69.
  25. ^ "daemons are not to be exorcised". The Unix Heritage Society mailing list archive. March 20, 2018. Retrieved October 25, 2026.
  26. ^ Pynchon, Thomas (1966). The Crying of Lot 49. J. B. Lippincott.
  27. ^ Lem, Stanisław (1974). The Cyberiad. Seabury Press.
  28. ^ "WHOIS record for demonpore.com". October 25, 2026.
  29. ^ a b Kemmishtree (March 28, 2026). "Welcome to my Minds". EQBio-OS.
  30. ^ "US10908144B2: Stacks of coaligned nanopores and fabrication and uses thereof". Google Patents. February 2, 2021. Retrieved October 25, 2026.
  31. ^ a b "Keltar's Field Guide to Molecular Reality". Molecular Reality Corporation. August 2026.
  32. ^ a b "Company records". Molecular Reality Corporation. October 2026.
  33. ^ Kemmishtree (March 29, 2026). "Flossing with DNA". EQBio-OS.
  34. ^ "refactor: Rename Daemon Pore/Sentinel to MR1 across codebase" (commit 2c06333). EpicQuestBio/MR1. October 18, 2026.

Further reading

  • Leff, H. S.; Rex, A. F. (ed.). Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing. Institute of Physics Publishing. 2003. ISBN 0-7503-0759-5.
Retrieved from "https://molecularreality.com/wiki/Maxwell%27s_demon"
Last edited 5 hours ago by PicoampPedant