Maxwell's demon is a

thought experiment A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences. History The ancient Greek ''deiknymi'' (), or thought experiment, "was the most anc ...

that would hypothetically violate the

second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unle ...

. It was proposed by the physicist

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

in 1867. In his first letter Maxwell called the

demon A demon is a malevolent supernatural entity. Historically, belief in demons, or stories about demons, occurs in religion, occultism, literature, fiction, mythology, and folklore; as well as in Media (communication), media such as comics, video ...

a "finite being", while the ''Daemon'' name was first used by Lord Kelvin. In the thought experiment, a demon controls a small massless door between two chambers of 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, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...

of the two gases, without applying any work, 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 a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ultim ...

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 natural phenomena. This is in contrast to experimental physics, which uses experim ...

, 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, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws ...

and

information theory Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. ...

. Most scientists argue, on theoretical grounds, that no practical 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 have 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 ...

wrote to Peter Guthrie Tait on 11 December 1867. It appeared again in a letter to

John William Strutt John William Strutt, 3rd Baron Rayleigh, (; 12 November 1842 – 30 June 1919) was an English mathematician and physicist who made extensive contributions to science. He spent all of his academic career at the University of Cambridge. A ...

in 1871, before it was presented to the public in Maxwell's 1872 book on

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". William Thomson (Lord Kelvin) was the first to use the word "demon" for Maxwell's concept, in the journal ''

Nature Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are ...

'' in 1874, and implied that he intended the

Greek mythology A major branch of classical mythology, Greek mythology is the body of myths originally told by the ancient Greeks, and a genre of Ancient Greek folklore. These stories concern the origin and nature of the world, the lives and activities o ...

interpretation of a daemon, 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 expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...

, 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 held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...

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 everyday use and 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 scalar quant ...

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 In thermodynamics and engineering, a heat engine is a system that converts heat to mechanical energy, which can then be used to do mechanical work. It does this by bringing a working substance from a higher state temperature to a lower stat ...

operating between the thermal reservoirs ''A'' and ''B'' could extract useful work 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 In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of ...

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 Rolf William Landauer (February 4, 1927 – April 27, 1999) was a German-American physicist who made important contributions in diverse areas of the thermodynamics of information processing, condensed matter physics, and the conductivity of dis ...

raised an exception to this argument. reprinted i
Vol. 44, No. 1, January 2000, p. 261
/ref> 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, 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 Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of t ...

, 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. 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

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 dependence between the two variables. More specifically, it quantifies the " amount of information" (in units such ...

) between the engine and the demon increases, and the feedback process is regarded as a process where the correlation decreases. If the correlation changes, thermodynamic relations as the second law of thermodynamics and the fluctuation theorem 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. These relations suggest that we need extra thermodynamic cost to increase correlation (measurement case), and in contrast we can apparently violate the second law up to the consumption of correlation (feedback case). For more general information processes including biological information processing, both inequality and equality with mutual information hold.

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, also shortened to nanotech, is the use of matter on an atomic, molecular, and supramolecular scale for industrial purposes. The earliest, widespread description of nanotechnology referred to the particular technological goal ...

. 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 the February 2007 issue of ''

'', David Leigh, a professor at the

University of Edinburgh The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 1 ...

, announced the creation of a nano-device based on the Brownian ratchet popularized by Richard Feynman. Leigh's device is able to drive a chemical system out of equilibrium, but it must be powered by an external source (

light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 t ...

in this case) and therefore does not violate thermodynamics. Previously, researchers including Nobel Prize winner Fraser Stoddart, 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 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 is not a true Maxwell's demon in the sense that it does not violate the

; it 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 Henry Brooks Adams (February 16, 1838 – March 27, 1918) was an American historian and a member of the Adams political family, descended from two U.S. Presidents. As a young Harvard graduate, he served as secretary to his father, Charles Fran ...

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 often compared wi ...

, 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 (derived ) is the systematic study and the documentation of the human activity. The time period of event before the invention of writing systems is considered prehistory. "History" is an umbrella term comprising past events as well ...

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 is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwee ...

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 published only 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 famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it ...

'', 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 * 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 Philosophy of thermal and statistical physics Nanotechnology James Clerk Maxwell Fictional demons and devils Thought experiments in physics Perpetual motion 1867 introductions