Maxwell's demon is a

thought experiment A thought experiment is an imaginary scenario that is meant to elucidate or test an argument or theory. It is often an experiment that would be hard, impossible, or unethical to actually perform. It can also be an abstract hypothetical that is ...

that appears to disprove the

second law of thermodynamics The second law of thermodynamics is a physical law based on Universal (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spont ...

. It was proposed by the physicist

James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician who was responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism an ...

in 1867. In his first letter, Maxwell referred to the entity as a "finite being" or a "being who can play a game of skill with the molecules".

Lord Kelvin William Thomson, 1st Baron Kelvin (26 June 182417 December 1907), was a British mathematician, Mathematical physics, mathematical physicist and engineer. Born in Belfast, he was the Professor of Natural Philosophy (Glasgow), professor of Natur ...

would later call it a "''

demon A demon is a malevolent supernatural entity. Historically, belief in demons, or stories about demons, occurs in folklore, mythology, religion, occultism, and literature; these beliefs are reflected in Media (communication), media including f ...

''". In the thought experiment, a demon controls a door between two chambers containing gas. As individual gas molecules (or atoms) approach the door, the demon quickly opens and closes the door to allow only fast-moving molecules to pass through in one direction, and only slow-moving molecules to pass through in the other. Because the kinetic temperature of a gas depends on the velocities of its constituent molecules, the demon's actions cause one chamber to warm up and the other to cool down. This would decrease the total

entropy Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the micros ...

of the

system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its open system (systems theory), environment, is described by its boundaries, str ...

, seemingly without applying any

work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an ani ...

, thereby violating the second law of thermodynamics. The concept of Maxwell's demon has provoked substantial debate in the

philosophy of science Philosophy of science is the branch of philosophy concerned with the foundations, methods, and implications of science. Amongst its central questions are the difference between science and non-science, the reliability of scientific theories, ...

and

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

, which continues to the present day. It stimulated work on the relationship between

thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

and

information theory Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...

. Most scientists argue that, on theoretical grounds, no device can violate the second law in this way. Other researchers have implemented forms of Maxwell's demon in experiments, though they all differ from the thought experiment to some extent and none has been shown to violate the second law.

Origin and history of the idea

The

first appeared in a letter

Maxwell Maxwell may refer to: People * Maxwell (surname), including a list of people and fictional characters with the name ** James Clerk Maxwell, mathematician and physicist * Justice Maxwell (disambiguation) * Maxwell baronets, in the Baronetage of N ...

wrote to Peter Guthrie Tait on 11 December 1867. It appeared again in a letter to John William Strutt in 1871, before it was presented to the public in Maxwell's 1872 book on thermodynamics titled ''Theory of Heat''. Leff & Rex (2002), p. 370. In his letters and books, Maxwell described the agent opening the door between the chambers as a "finite being". Being a deeply religious man, he never used the word "demon". Instead, William Thomson (Lord Kelvin) was the first to use it for Maxwell's concept, in the journal ''

Nature Nature is an inherent character or constitution, particularly of the Ecosphere (planetary), ecosphere or the universe as a whole. In this general sense nature refers to the Scientific law, laws, elements and phenomenon, phenomena of the physic ...

'' in 1874, and implied that he intended the

Greek mythology Greek mythology is the body of myths originally told by the Ancient Greece, ancient Greeks, and a genre of ancient Greek folklore, today absorbed alongside Roman mythology into the broader designation of classical mythology. These stories conc ...

interpretation of a

daemon A demon is a malevolent supernatural being, evil spirit or fiend in religion, occultism, literature, fiction, mythology and folklore. Demon, daemon or dæmon may also refer to: Entertainment Fictional entities * Daemon (G.I. Joe), a character ...

, a supernatural being working in the background, rather than a malevolent being.

Original thought experiment

The second law of thermodynamics ensures (through statistical probability) that two bodies of different

temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...

, 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 In physical science, an isolated system is either of the following: # a physical system so far removed from other systems that it does not interact with them. # a thermodynamic system enclosed by rigid immovable walls through which neither ...

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:Maxwell (1871), reprinted in Leff & Rex (1990) on p. 4. 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

molecule A molecule is a group of two or more atoms that are held together by Force, attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemi ...

s on both sides, an imaginary

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 In kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a non-negative scalar quantity. Intro ...

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. A

heat engine A heat engine is a system that transfers thermal energy to do mechanical or electrical work. While originally conceived in the context of mechanical energy, the concept of the heat engine has been applied to various other kinds of energy, pa ...

operating between the thermal reservoirs ''A'' and ''B'' could extract useful

from this temperature difference. 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.

Criticism and development

Several physicists have presented calculations that show that the

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 thermodynamic work to gauge the speed of the molecules and selectively allow them to pass through the opening between ''A'' and ''B'' than the amount of

energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...

gained by the difference of temperature caused by doing so. One of the most famous responses to this question was suggested in 1929 by Leó Szilárd, cited in Bennett 1987. English translation available a
NASA document TT F-16723
published 1976 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. reprinted i
Vol. 44, No. 1, January 2000, p. 261
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 entropy in thermodynamics and information theory, 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, Charles 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. Regarding Landauer's principle, the minimum energy dissipated by deleting information was experimentally measured by Eric Lutz ''et al.'' in 2012. Furthermore, Lutz ''et al.'' confirmed that in order to approach the Landauer's limit, the system must asymptotically approach zero processing speed. Recently, Landauer's principle has also been invoked to resolve an apparently unrelated paradox of statistical physics, Loschmidt’s paradox. John Earman and John D. Norton have argued that Szilárd and Landauer's explanations of Maxwell's demon begin by assuming that the

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.

Recent progress

Although the argument by Landauer and Bennett only answers the consistency between the second law of thermodynamics and the whole cyclic process of the entire system of a Szilard engine (a composite system of the engine and the demon), a recent approach based on the non-equilibrium thermodynamics for small fluctuating systems has provided deeper insight on each information process with each subsystem. From this viewpoint, the measurement process is regarded as a process where the correlation (

mutual information In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual Statistical dependence, dependence between the two variables. More specifically, it quantifies the "Information conten ...

) between the engine and the demon increases, decreasing the entropy of the system in an amount given by the mutual information. If the correlation changes, thermodynamic relations such as the second law of thermodynamics and the

fluctuation theorem The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the Entropy (statistical thermodynamics), entropy of a system which is currently away from thermodynamic equilibrium (i.e., maxim ...

for each subsystem should be modified, and for the case of external control a second-law like inequality and a generalized fluctuation theorem with mutual information are satisfied. For more general information processes including biological information processing, both inequality and equality with mutual information hold. When repeated measurements are performed, the entropy reduction of the system is given by the entropy of the sequence of measurements, which takes into account the reduction of information due to the correlation between the measurements. More recently, Kastner has argued that the uncertainty principle forces an entropy increase when the molecule is localized to one side or the other in the Szilard engine, and that is what prevents the demon from violating the second law. For the case of the original Demon who is sorting molecules by speeds, Kastner and Schlatter argue that the uncertainty principle prevents the Demon from sorting the molecules due to their delocalization upon measurement of momentum.

Applications

Real-life versions of Maxwellian demons occur, but all such "real demons" or molecular demons have their entropy-lowering effects duly balanced by increase of entropy elsewhere. Molecular-sized mechanisms are no longer found only in biology; they are also the subject of the emerging field of

nanotechnology Nanotechnology is the manipulation of matter with at least one dimension sized from 1 to 100 nanometers (nm). At this scale, commonly known as the nanoscale, surface area and quantum mechanical effects become important in describing propertie ...

. 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. 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."

Experimental work

In 2007, David Leigh announced the creation of a nano-device based on the Brownian ratchet popularized by

Richard Feynman Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist. He is best known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of t ...

. Leigh's device is able to drive a chemical system out of equilibrium, but it must be powered by an external source (

light Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...

in this case) and therefore does not violate thermodynamics. Previously, researchers including Nobel Prize winner

Fraser Stoddart Sir James Fraser Stoddart, (24 May 1942 – 30 December 2024) was a British-American chemist who was Chair Professor in Chemistry at the University of Hong Kong. He was the Board of Trustees Professor of Chemistry and head of the Stoddart ...

had created ring-shaped molecules called rotaxanes which could be placed on an axle connecting two sites, ''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, restricting the motion of the ring. It keeps the ring from moving, however, only if it is at ''A''. Over time, therefore, the rings will be bumped from ''B'' to ''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. In 2009, Mark G. Raizen developed a laser atomic cooling technique which realizes the process Maxwell envisioned of sorting individual atoms in a gas into different containers based on their energy. The new concept is a one-way wall for atoms or molecules that allows them to 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 using 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 for regulating the 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 other

laser cooling Laser cooling includes several techniques where atoms, molecules, and small mechanical systems are cooled with laser light. The directed energy of lasers is often associated with heating materials, e.g. laser cutting, so it can be counterintuit ...

techniques which use the momentum of the photon and require 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 by the one-way wall. This technique is widely described as a "Maxwell's demon" because it realizes Maxwell's process of creating a temperature difference by sorting high and low energy atoms into different containers. However, scientists have pointed out that it does not violate the

, does not result in a net decrease in entropy, and cannot be used to produce useful energy. This is because the process requires more energy from the laser beams than could be produced by the temperature difference generated. The atoms absorb low entropy photons from the laser beam and emit them in a random direction, thus increasing the entropy of the environment. In 2014, Pekola et al. demonstrated an experimental realization of a Szilárd engine. Only a year later and based on an earlier theoretical proposal, the same group presented the first experimental realization of an autonomous Maxwell's demon, which extracts microscopic information from a system and reduces its entropy by applying feedback. The demon is based on two capacitively coupled single-electron devices, both integrated on the same electronic circuit. The operation of the demon is directly observed as a temperature drop in the system, with a simultaneous temperature rise in the demon arising from the thermodynamic cost of generating the mutual information. In 2016, Pekola et al. demonstrated a proof-of-principle of an autonomous demon in coupled single-electron circuits, showing a way to cool critical elements in a circuit with information as a fuel. Pekola et al. have also proposed that a simple qubit circuit, e.g., made of a superconducting circuit, could provide a basis to study a quantum Szilard's engine.

As metaphor

Daemons in computing, generally processes that run on servers to respond to users, are named for Maxwell's demon. Historian Henry Brooks Adams, in his manuscript '' The Rule of Phase Applied to History'', attempted to use Maxwell's demon as a historical

metaphor A metaphor is a figure of speech that, for rhetorical effect, directly refers to one thing by mentioning another. It may provide, or obscure, clarity or identify hidden similarities between two different ideas. Metaphors are usually meant to cr ...

, though he misunderstood and misapplied the original principle. Cater (1947), pp. 640–647; see also Daub (1970), reprinted in Leff & Rex (1990), pp. 37–51. Adams interpreted

history History is the systematic study of the past, focusing primarily on the Human history, human past. As an academic discipline, it analyses and interprets evidence to construct narratives about what happened and explain why it happened. Some t ...

as a process moving towards "equilibrium", but he saw militaristic nations (he felt

Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...

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 his death in 1918 and was published posthumously. Adams (1919), p. 267.

Notes

References

* * * * *

External links

How Maxwell's Demon Continues to Startle Scientists
* Bennett, C. H. (1987) "Demons, Engines and the Second Law", ''

Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it, with more than 150 Nobel Pri ...

'', November, ''pp''108-116 * * * * * * * Maroney, O. J. E. (2009)
"Information Processing and Thermodynamic Entropy
The Stanford Encyclopedia of Philosophy (Autumn 2009 Edition) * , reprinted (2001) New York: Dover, * {{cite journal, author=Norton, J., year=2005, title=Eaters of the lotus: Landauer's principle and the return of Maxwell's demon, journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, volume=36, issue=2, pages=375–411, doi=10.1016/j.shpsb.2004.12.002, url=http://philsci-archive.pitt.edu/archive/00001729/02/Norton.pdf, archive-url=https://web.archive.org/web/20060901211014/http://philsci-archive.pitt.edu/archive/00001729/02/Norton.pdf, archive-date=2006-09-01, url-status=live, bibcode=2005SHPMP..36..375N, citeseerx=10.1.1.468.3017, s2cid=21104635 * Raizen, Mark G. (2011) "Demons, Entropy, and the Quest for Absolute Zero", ''

, ''March, ''pp''54-59 * Reaney, Patricia
"Scientists build nanomachine"
''Reuters'', February 1, 2007 * Rubi, J Miguel,
Does Nature Break the Second Law of Thermodynamics?
; Scientific American, October 2008 : * Splasho (2008) �
Historical development of Maxwell's demon
* Weiss, Peter
"Breaking the Law – Can quantum mechanics + thermodynamics = perpetual motion?"
''Science News'', October 7, 2000 1867 introductions Fictional demons James Clerk Maxwell Nanotechnology Perpetual motion Philosophy of thermal and statistical physics Thought experiments in physics