Maxwell's demon
Encyclopedia
In the philosophy of thermal and statistical physics
, Maxwell's demon is a thought experiment
created by the Scottish
physicist
James Clerk Maxwell
to "show that the Second Law of Thermodynamics
has only a statistical certainty." It demonstrates Maxwell
's point by hypothetically describing how to violate the Second Law: A container is divided into two parts by an insulated wall, with a door that can be opened and closed by what came to be called "Maxwell's demon"; the demon
opens the door to allow only the "hot" molecules of gas to flow through to a favored side of the chamber, causing that side to gradually heat up while the other side cools down.
first appeared in a letter Maxwell
wrote to Peter Guthrie Tait
on 11 December 1867. It appeared again in a letter to John William Strutt in 1870, before it was presented to the public in Maxwell's 1871 book on thermodynamics
titled Theory of Heat.
In his letters and book, 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 in 1874, and implied that he intended the mediating, rather than malevolent, connotation of the word.
, 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
, entropy
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:
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
s on both sides, an imaginary demon
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
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.
Note that 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. In fact, because temperature and pressure are related, if A and B both contain the same numbers of molecule per unit volume, the one with the higher temperature will also have higher pressure; the demon must actually let more slow molecules pass from B to A than fast ones pass from A to B in order to make B hotter at the same pressure. In fact, by regulating the number of molecules passed in each direction, the demon could achieve a pressure difference instead of a temperature difference, or any combination of temperature and pressure differences (possibly including lower pressure on the higher temperature side, depending on the variance in the speeds of the molecules).
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 energy to gauge the speed of the molecules and allow them to selectively pass through the opening between A and B than the amount of energy saved by the difference of temperature caused by this.
One of the most famous responses to this question was suggested in 1929 by Leó Szilárd
, 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. 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, 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.
However, John Earman
and John Norton have argued that Szilárd and Landauer's explanations of Maxwell's Demon begin by assuming that the second law of thermodynamics
cannot be violated, thus rendering their proofs that Maxwell's Demon cannot violate the Second Law circular.
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.
Molecular-sized mechanisms are no longer found only in biology; they are also the subject of the emerging field of nanotechnology
.
A large-scale, commercially-available pneumatic device, called a Ranque-Hilsch vortex tube
separates hot and cold air. It sorts molecules by exploiting the conservation of angular momentum: hotter molecules are spun to the outside of the tube while cooler molecules spin in a tighter whirl within the tube. Gas from the two different temperature whirls may be vented on opposite ends of the tube. Although this creates a temperature difference, the energy to do so is supplied by the pressure driving the gas through the tube.
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."
In 1962 lectures, to illustrate thermodynamics, physicist Richard Feynman
analyzed a putative Maxwell's demon device, a tiny paddlewheel attached to a ratchet
, showing why it cannot extract energy from molecular motion of a fluid at equilibrium. This brownian ratchet
is a popular teaching tool.
, David Leigh
, a professor at the University of Edinburgh
, announced the creation of a nano-device based on this thought experiment. This device is able to drive a chemical system out of equilibrium
, but it must be powered by an external source (light
in this case) and therefore does not violate thermodynamics.
Previously, other researchers created a ring-shaped molecule which could be placed on an axle connecting two sites (called 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, thus restricting the motion of the ring. It only keeps the ring from moving, however, if it is at site A. Over time, therefore, the rings will be bumped from site B to site 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.
The March 2011 issue of Scientific American
features an article by Professor Mark G. Raizen
of the University of Texas, Austin which discusses the first realization of Maxwell's Demon with gas phase particles, as originally envisioned by Maxwell. In 2005, Raizen and collaborators showed how to realize Maxwell's Demon for an ensemble of dilute gas-phase atoms or molecules. The new concept is a one-way wall for atoms or molecules that allows them 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 to use 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 to regulate 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 laser cooling which uses the momentum of the photon and requires 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 with the one-way wall. Therefore, single-photon cooling is a physical realization of Maxwell’s Demon in the same sense envisioned by Leo Szilard in 1929.
The importance of single photon cooling is that it provides a general method for cooling multi-level atoms or molecules. It circumvents the limitation of laser cooling which requires a two-level cycling transition, and hence is limited to a small set of atoms in the Periodic Table
. The experimental realization of Maxwell's Demon is a key step towards general control of atoms in gas phase. Beyond basic scientific research, these methods will enable efficient isotope separation for medicine and basic research, as well as controlling atoms in gas phase for nanoscale deposition on surfaces. This new, bottom-up, approach to nanoscience is called Atomoscience
and is enabled by the realization of Maxwell's Demon.
, though he misunderstood and misapplied the original principle. Adams interpreted history
as a process moving towards "equilibrium", but he saw militaristic
nations (he felt Germany
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 only published posthumously.
In the way of short stories, a homage to Maxwell has been written by Isaac Asimov
and Larry Niven
. Additionally, Larry Niven's Warlock in The Magic Goes Away
uses such a demon to cool his home in a vignette titled "Unfinished Story #1" as published in Playgrounds of the Mind
(and, earlier, in All the Myriad Ways
). The Demon also contributes to the thesis of Ken Kesey's
collection of stories, The Demon Box. In the story "A Feast of Demons" by William Morrison (pseudonym for Joseph Samachson
), a scientist creates Maxwell's Demons to change the temperature of items, the purity of ores, and eventually even reverse or accelerate the aging process in people—only to have the Demons escape and wreak havoc on civilization. An implementation of a scientifically plausible nanotech version of Maxwell's demon appears in Paul Di Filippo's
short story Any Major Dude, the use of which gives a country in the story the name "Maxwell's Land" and its inhabitants "demons."
In music and film, Maxwell Demon was the name of Brian Eno's
first band, which was the inspiration for the name of a fictional character in the film Velvet Goldmine
, and "Maxwell's Demon" is the name of a 1968 film by the American experimental filmmaker Hollis Frampton
. Maxwell's Demon is mentioned in the song "A Metaphysical Drama" by Vintersorg and also is the name of a Brooklyn-based indie rock band, as well as that of a London alt-pop band. See also the lyrics to "Isaac's Law" by The Loud Family.
Citing Maxwell's Demon, mathematicians philosophized about the actions of an escaped criminal in the American television program Numb3rs
. The episode, titled "Arrow of Time", was episode 11 of season 5, and originally aired on January 9, 2009.
A Mac Hall
comic depicts the character Matt hallucinating a demon named Maxwell who lives in the air conditioner replacing hot air molecules with cool ones. He claims to refute the second law of thermodynamics
. The demon's work in progress can be seen in a lighter note in an Abstruse Goose comic.
Maxwell's Demon was a vital element in the plot of the anime series El Cazador de la Bruja
. Scientists recreated what was believed to be an extinct breed of humans capable of interacting with Maxwell's Demon and branded them the name of witches. The deuteragonist of the series, Ellis, was one such witch.
James K. Galbraith's
book The Predator State: How Conservatives Abandoned the Free Market and Why Liberals Should Too describes the market as "a disembodied decision maker — a Maxwell's Demon — that, somehow, and without effort, balances and reflects the preferences of everyone participating in economic decisions... It can be these things precisely because it is nothing at all." (Galbraith 19-20)
UK drum and bass producer John B titled a song on his Visions album "Maxwell's Demon".
Philosophy of thermal and statistical physics
The philosophy of thermal and statistical physics is that part of the philosophy of physics whose subject matter is classical thermodynamics, statistical mechanics, and related theories...
, Maxwell's demon is a thought experiment
Thought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...
created by the Scottish
Scotland
Scotland is a country that is part of the United Kingdom. Occupying the northern third of the island of Great Britain, it shares a border with England to the south and is bounded by the North Sea to the east, the Atlantic Ocean to the north and west, and the North Channel and Irish Sea to the...
physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
James Clerk Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...
to "show that the Second Law of Thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
has only a statistical certainty." It demonstrates Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...
's point by hypothetically describing how to violate the Second Law: A container is divided into two parts by an insulated wall, with a door that can be opened and closed by what came to be called "Maxwell's demon"; the demon
Demon
call - 1347 531 7769 for more infoIn Ancient Near Eastern religions as well as in the Abrahamic traditions, including ancient and medieval Christian demonology, a demon is considered an "unclean spirit" which may cause demonic possession, to be addressed with an act of exorcism...
opens the door to allow only the "hot" molecules of gas to flow through to a favored side of the chamber, causing that side to gradually heat up while the other side cools down.
Origin and history of the idea
The thought experimentThought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...
first appeared in a letter Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...
wrote to Peter Guthrie Tait
Peter Guthrie Tait
Peter Guthrie Tait FRSE was a Scottish mathematical physicist, best known for the seminal energy physics textbook Treatise on Natural Philosophy, which he co-wrote with Kelvin, and his early investigations into knot theory, which contributed to the eventual formation of topology as a mathematical...
on 11 December 1867. It appeared again in a letter to John William Strutt in 1870, before it was presented to the public in Maxwell's 1871 book on thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
titled Theory of Heat.
In his letters and book, Maxwell described the agent opening the door between the chambers as a "finite being."
William Thomson (Lord Kelvin)
William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...
was the first to use the word "demon" for Maxwell's concept, in the journal Nature in 1874, and implied that he intended the mediating, rather than malevolent, connotation of the word.
Original thought experiment
The second law of thermodynamics ensures (through statistical probability) that two bodies of different temperatureTemperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
, 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
Isolated system
In the natural sciences an isolated system, as contrasted with an open system, is a physical system without any external exchange. If it has any surroundings, it does not interact with them. It obeys in particular the first of the conservation laws: its total energy - mass stays constant...
, entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
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:
Gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...
at equal temperatures and placed next to each other. Observing the molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
s on both sides, an imaginary demon
Demon
call - 1347 531 7769 for more infoIn Ancient Near Eastern religions as well as in the Abrahamic traditions, including ancient and medieval Christian demonology, a demon is considered an "unclean spirit" which may cause demonic possession, to be addressed with an act of exorcism...
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
Speed
In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...
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.
Note that 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. In fact, because temperature and pressure are related, if A and B both contain the same numbers of molecule per unit volume, the one with the higher temperature will also have higher pressure; the demon must actually let more slow molecules pass from B to A than fast ones pass from A to B in order to make B hotter at the same pressure. In fact, by regulating the number of molecules passed in each direction, the demon could achieve a pressure difference instead of a temperature difference, or any combination of temperature and pressure differences (possibly including lower pressure on the higher temperature side, depending on the variance in the speeds of the molecules).
Criticism and development
Several physicists have presented calculations that show that the second law of thermodynamicsSecond law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
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 energy to gauge the speed of the molecules and allow them to selectively pass through the opening between A and B than the amount of energy saved by the difference of temperature caused by this.
One of the most famous responses to this question was suggested in 1929 by Leó Szilárd
Leó Szilárd
Leó Szilárd was an Austro-Hungarian physicist and inventor who conceived the nuclear chain reaction in 1933, patented the idea of a nuclear reactor with Enrico Fermi, and in late 1939 wrote the letter for Albert Einstein's signature that resulted in the Manhattan Project that built the atomic bomb...
, and later by Léon Brillouin
Léon Brillouin
Léon Nicolas Brillouin was a French physicist. He made contributions to quantum mechanics, radio wave propagation in the atmosphere, solid state physics, and information theory.-Early life:...
. 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 Landauer
Rolf William Landauer was an IBM physicist who in 1961 argued that when information is lost in an irreversible circuit, the information becomes entropy and an associated amount of energy is dissipated as heat...
raised an exception to this argument. He realized that some measuring processes need not increase thermodynamic entropy as long as they were thermodynamically reversible
Reversible process (thermodynamics)
In thermodynamics, a reversible process, or reversible cycle if the process is cyclic, is a process that can be "reversed" by means of infinitesimal changes in some property of the system without loss or dissipation of energy. Due to these infinitesimal changes, the system is in thermodynamic...
. 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
Information entropy
In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits...
, 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, Bennett
Charles H. Bennett (computer scientist)
Charles H. Bennett is an IBM Fellow at IBM Research. Bennett's recent work at IBM has concentrated on a re-examination of the physical basis of information, applying quantum physics to the problems surrounding information exchange...
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.
However, John Earman
John Earman
John Earman is a philosopher of physics. He is currently an emeritus professor in the History and Philosophy of Science department at the University of Pittsburgh. He has also taught at UCLA, the Rockefeller University, and the University of Minnesota, and was president of the Philosophy of...
and John Norton have argued that Szilárd and Landauer's explanations of Maxwell's Demon begin by assuming that the second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
cannot be violated, thus rendering their proofs that Maxwell's Demon cannot violate the Second Law circular.
Applications
Real-life versions of Maxwellian demons occur, but all such "real demons" have their entropy-lowering effects duly balanced by increase of entropy elsewhere.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.
Molecular-sized mechanisms are no longer found only in biology; they are also the subject of the emerging field of nanotechnology
Nanotechnology
Nanotechnology is the study of manipulating matter on an atomic and molecular scale. Generally, nanotechnology deals with developing materials, devices, or other structures possessing at least one dimension sized from 1 to 100 nanometres...
.
A large-scale, commercially-available pneumatic device, called a Ranque-Hilsch vortex tube
Vortex tube
The vortex tube, also known as the Ranque-Hilsch vortex tube, is a mechanical device that separates a compressed gas into hot and cold streams. It has no moving parts....
separates hot and cold air. It sorts molecules by exploiting the conservation of angular momentum: hotter molecules are spun to the outside of the tube while cooler molecules spin in a tighter whirl within the tube. Gas from the two different temperature whirls may be vented on opposite ends of the tube. Although this creates a temperature difference, the energy to do so is supplied by the pressure driving the gas through the tube.
If hypothetical mirror matter
Mirror matter
In physics, mirror matter, also called shadow matter or Alice matter, is a hypothetical counterpart to ordinary matter.Modern physics deals with three basic types of spatial symmetry: reflection, rotation and translation. The known elementary particles respect rotation and translation symmetry but...
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."
In 1962 lectures, to illustrate thermodynamics, physicist Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...
analyzed a putative Maxwell's demon device, a tiny paddlewheel attached to a ratchet
Ratchet (device)
A ratchet is a device that allows continuous linear or rotary motion in only one direction while preventing motion in the opposite direction. Because most socket wrenches today use ratcheting handles, the term "ratchet" alone is often used to refer to a ratcheting wrench, and the terms "ratchet"...
, showing why it cannot extract energy from molecular motion of a fluid at equilibrium. This brownian ratchet
Brownian ratchet
In the philosophy of thermal and statistical physics, the Brownian ratchet, or Feynman-Smoluchowski ratchet is a thought experiment about an apparent perpetual motion machine first analysed in 1912 by Polish physicist Marian Smoluchowski and popularised by American Nobel laureate physicist Richard...
is a popular teaching tool.
Experimental work
In the 1 February 2007 issue of NatureNature (journal)
Nature, first published on 4 November 1869, is ranked the world's most cited interdisciplinary scientific journal by the Science Edition of the 2010 Journal Citation Reports...
, David Leigh
David Leigh (scientist)
David Alan Leigh FRS is the Forbes Professor of Organic Chemistry at the University of Edinburgh.He is noted for the development of new methods to construct rotaxanes, catenanes and molecular knots and for the invention of some of the first synthetic molecular motors and functional nanomachines...
, a professor at the University of Edinburgh
University of Edinburgh
The University of Edinburgh, founded in 1583, is a public research university located in Edinburgh, the capital of Scotland, and a UNESCO World Heritage Site. The university is deeply embedded in the fabric of the city, with many of the buildings in the historic Old Town belonging to the university...
, announced the creation of a nano-device based on this thought experiment. This device is able to drive a chemical system out of equilibrium
Chemical equilibrium
In a chemical reaction, chemical equilibrium is the state in which the concentrations of the reactants and products have not yet changed with time. It occurs only in reversible reactions, and not in irreversible reactions. Usually, this state results when the forward reaction proceeds at the same...
, but it must be powered by an external source (light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
in this case) and therefore does not violate thermodynamics.
Previously, other researchers created a ring-shaped molecule which could be placed on an axle connecting two sites (called 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, thus restricting the motion of the ring. It only keeps the ring from moving, however, if it is at site A. Over time, therefore, the rings will be bumped from site B to site 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.
The March 2011 issue of Scientific American
Scientific American
Scientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...
features an article by Professor Mark G. Raizen
Mark G. Raizen
Mark George Raizen is a physicist who conducts experiments on quantum optics and atom optics.-Birth and Education:Raizen was born in New York City where generations of his family resided since the 1840s. While he comes from a long line of medical doctors, dating back to the Civil War, Raizen's life...
of the University of Texas, Austin which discusses the first realization of Maxwell's Demon with gas phase particles, as originally envisioned by Maxwell. In 2005, Raizen and collaborators showed how to realize Maxwell's Demon for an ensemble of dilute gas-phase atoms or molecules. The new concept is a one-way wall for atoms or molecules that allows them 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 to use 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 to regulate 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 laser cooling which uses the momentum of the photon and requires 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 with the one-way wall. Therefore, single-photon cooling is a physical realization of Maxwell’s Demon in the same sense envisioned by Leo Szilard in 1929.
The importance of single photon cooling is that it provides a general method for cooling multi-level atoms or molecules. It circumvents the limitation of laser cooling which requires a two-level cycling transition, and hence is limited to a small set of atoms in the Periodic Table
Periodic table
The periodic table of the chemical elements is a tabular display of the 118 known chemical elements organized by selected properties of their atomic structures. Elements are presented by increasing atomic number, the number of protons in an atom's atomic nucleus...
. The experimental realization of Maxwell's Demon is a key step towards general control of atoms in gas phase. Beyond basic scientific research, these methods will enable efficient isotope separation for medicine and basic research, as well as controlling atoms in gas phase for nanoscale deposition on surfaces. This new, bottom-up, approach to nanoscience is called Atomoscience
Atomoscience
- Atomoscience :Atomoscience is the field enabled by the development of general methods to control atomic motion in gas phase. Atomoscience is a "bottom up" approach to building complexity, and is complementary to Nanoscience, typically, a top-down approach. Mark G. Raizen proposed Atomoscience as...
and is enabled by the realization of Maxwell's Demon.
Adams and the demon as historical metaphor
Historian Henry Brooks Adams in his manuscript The Rule of Phase Applied to History attempted to use Maxwell's demon as a historical metaphorMetaphor
A metaphor is a literary figure of speech that uses an image, story or tangible thing to represent a less tangible thing or some intangible quality or idea; e.g., "Her eyes were glistening jewels." Metaphor may also be used for any rhetorical figures of speech that achieve their effects via...
, though he misunderstood and misapplied the original principle. Adams interpreted history
History
History is the discovery, collection, organization, and presentation of information about past events. History can also mean the period of time after writing was invented. Scholars who write about history are called historians...
as a process moving towards "equilibrium", but he saw militaristic
Militarism
Militarism is defined as: the belief or desire of a government or people that a country should maintain a strong military capability and be prepared to use it aggressively to defend or promote national interests....
nations (he felt Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
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 only published posthumously.
In popular culture
In literature, Maxwell’s Demon appears in- Thomas Pynchon'sThomas PynchonThomas Ruggles Pynchon, Jr. is an American novelist. For his most praised novel, Gravity's Rainbow, Pynchon received the National Book Award, and is regularly cited as a contender for the Nobel Prize in Literature...
novels, The Crying of Lot 49The Crying of Lot 49The Crying of Lot 49 is a novel by Thomas Pynchon, first published in 1966. The shortest of Pynchon's novels, it is about a woman, Oedipa Maas, possibly unearthing the centuries-old conflict between two mail distribution companies, Thurn und Taxis and the Trystero...
and Gravity's RainbowGravity's RainbowGravity's Rainbow is a postmodern novel written by Thomas Pynchon and first published on February 28, 1973.The narrative is set primarily in Europe at the end of World War II and centers on the design, production and dispatch of V-2 rockets by the German military, and, in particular, the quest...
, - George Gamow'sGeorge GamowGeorge Gamow , born Georgiy Antonovich Gamov , was a Russian-born theoretical physicist and cosmologist. He discovered alpha decay via quantum tunneling and worked on radioactive decay of the atomic nucleus, star formation, stellar nucleosynthesis, Big Bang nucleosynthesis, cosmic microwave...
Mr. Tompkins. - It is mentioned in the novel Homo FaberHomo Faber (novel)Homo Faber is a novel by Max Frisch, first published in Germany in 1957. The first English edition was published in England in 1959. The novel is written as a first-person narrative. The protagonist, Walter Faber, is a successful engineer traveling throughout Europe and the Americas on behalf of...
by SwissSwitzerlandSwitzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....
author Max FrischMax FrischMax Rudolf Frisch was a Swiss playwright and novelist, regarded as highly representative of German-language literature after World War II. In his creative works Frisch paid particular attention to issues relating to problems of human identity, individuality, responsibility, morality and political... - Also mentioned in one of the short stories of The CyberiadThe CyberiadThe Cyberiad is a series of humorous short stories by Stanisław Lem. The Polish version was first published in 1965, with an English translation appearing in 1974. The main protagonists of the series are Trurl and Klapaucius, the "constructors"....
by Stanisław Lem: "The Sixth Sally, or How Trurl and Klaupacius Created a Demon of the Second Kind to Defeat the Pirate Pugg". - In Greg Egan's hard science fiction novel Permutation City, Maxwell's Demon is the name of a program used by the character Maria to keep track of individual "molecules" in the cellular automaton known as the Autoverse.
- Maxwell's Demon appears, and fills his typical role, in the climax of the book Master of the Five MagicsMaster of the Five MagicsMaster of the Five Magics is a fantasy novel by Lyndon Hardy, first published in 1980. It is the first of a trilogy set in the same world; the second book is Secret of the Sixth Magic and the third Riddle of the Seven Realms...
by Lyndon HardyLyndon HardyLyndon Maurice Hardy is an American physicist, fantasy author, and business owner.-Biography:He is a member of the Science Fiction Writers of America. He attended California Institute of Technology as an undergraduate and the University of California Berkeley for his Ph.D.In his college years he...
. - Maxwell's Demon was also mentioned in Christopher Stasheff'sChristopher StasheffChristopher Stasheff is an American science fiction author and fantasy author whose novels include The Warlock in Spite of Himself and Her Majesty's Wizard . He has a PhD. in Theatre and also teaches radio and television at Eastern New Mexico University in New Mexico...
books from the series A Wizard in Rhyme, wherein he let Maxwell's Demon (Max for short) help out the main character. - In Arkady and Boris Strugatsky'sArkady and Boris StrugatskyThe brothers Arkady and Boris Strugatsky are Soviet Jewish-Russian science fiction authors who collaborated on their fiction.-Life and work:...
book Monday Begins on SaturdayMonday Begins on SaturdayMonday Begins on Saturday is a 1964 science fiction / science fantasy novel by Boris and Arkady Strugatsky. Set in a fictional town in northern Russia, where highly classified research in magic occurs, the novel is a satire of Soviet scientific research institutes, complete with an inept...
two of Maxwell's demons work as doormen in the Institute for Magic and Thaumaturgy.
In the way of short stories, a homage to Maxwell has been written by Isaac Asimov
Isaac Asimov
Isaac Asimov was an American author and professor of biochemistry at Boston University, best known for his works of science fiction and for his popular science books. Asimov was one of the most prolific writers of all time, having written or edited more than 500 books and an estimated 90,000...
and Larry Niven
Larry Niven
Laurence van Cott Niven / ˈlæri ˈnɪvən/ is an American science fiction author. His best-known work is Ringworld , which received Hugo, Locus, Ditmar, and Nebula awards. His work is primarily hard science fiction, using big science concepts and theoretical physics...
. Additionally, Larry Niven's Warlock in The Magic Goes Away
The Magic Goes Away
The Magic Goes Away is a fantasy short story written by Larry Niven in 1976, and later expanded to a novella of the same name which was published in 1978...
uses such a demon to cool his home in a vignette titled "Unfinished Story #1" as published in Playgrounds of the Mind
Playgrounds of the Mind
Playgrounds of the Mind is a collection of short stories by Larry Niven, published in 1991. It is the sequel to N-Space.Many of the stories are set in Niven's Known Space universe...
(and, earlier, in All the Myriad Ways
All the Myriad Ways
All the Myriad Ways is a collection of 14 short stories and essays by science fiction author Larry Niven, originally published in 1971.-Contents:* "All the Myriad Ways"* "Passerby"* "For a Foggy Night"* "Wait it Out"* "The Jigsaw Man"...
). The Demon also contributes to the thesis of Ken Kesey's
Ken Kesey
Kenneth Elton "Ken" Kesey was an American author, best known for his novel One Flew Over the Cuckoo's Nest , and as a counter-cultural figure who considered himself a link between the Beat Generation of the 1950s and the hippies of the 1960s. "I was too young to be a beatnik, and too old to be a...
collection of stories, The Demon Box. In the story "A Feast of Demons" by William Morrison (pseudonym for Joseph Samachson
Joseph Samachson
Dr. Joseph "Joe" Samachson was a scientist and author, primarily of science fiction and comic books.-Biochemist:Joseph Samachson was born to David and Anna Samachson on October 13, 1906 in Trenton, New Jersey. A graduate of Rutgers University, he earned a Ph.D. in Chemistry from Yale at the age of...
), a scientist creates Maxwell's Demons to change the temperature of items, the purity of ores, and eventually even reverse or accelerate the aging process in people—only to have the Demons escape and wreak havoc on civilization. An implementation of a scientifically plausible nanotech version of Maxwell's demon appears in Paul Di Filippo's
Paul Di Filippo
Paul Di Filippo is an American science fiction writer. He has been published in Postscripts...
short story Any Major Dude, the use of which gives a country in the story the name "Maxwell's Land" and its inhabitants "demons."
In music and film, Maxwell Demon was the name of Brian Eno's
Brian Eno
Brian Peter George St. John le Baptiste de la Salle Eno , commonly known as Brian Eno or simply as Eno , is an English musician, composer, record producer, singer and visual artist, known as one of the principal innovators of ambient music.Eno studied at Colchester Institute art school in Essex,...
first band, which was the inspiration for the name of a fictional character in the film Velvet Goldmine
Velvet Goldmine
Velvet Goldmine is a 1998 British/American drama film directed and co-written by Todd Haynes. The film tells the story of a pop star based mainly on David Bowie's 'Ziggy Stardust' character and is set in Britain during the days of glam rock in the early 1970s.Sandy Powell received another Academy...
, and "Maxwell's Demon" is the name of a 1968 film by the American experimental filmmaker Hollis Frampton
Hollis Frampton
Hollis Frampton was an American avant-garde filmmaker, photographer, writer/theoretician, and pioneer of digital art.-Early years:Frampton was born March 11, 1936 in Wooster, Ohio...
. Maxwell's Demon is mentioned in the song "A Metaphysical Drama" by Vintersorg and also is the name of a Brooklyn-based indie rock band, as well as that of a London alt-pop band. See also the lyrics to "Isaac's Law" by The Loud Family.
- The computer game Maxwell's ManiacMaxwell's ManiacMaxwell's Maniac is a computer game originally part of the Microsoft Entertainment Pack series. Loosely based on the concept of Maxwell's demon, the object is to separate red and blue molecules into their respective color-coded chambers, using a sliding door...
from Microsoft Entertainment PackMicrosoft Entertainment PackThe original Microsoft Windows Entertainment Pack is a collection of simply-designed 16-bit computer games for Windows. These games were somewhat unusual for the time, in that they would not run under MS-DOS. Many of the games were later released in the Best of Windows Entertainment Pack...
is loosely based on Maxwell's Demon. - In the .Hack.hack.hack is a Japanese multimedia franchise that encompasses two projects; Project .hack and .hack Conglomerate. Both projects were primarily created/developed by CyberConnect2, and published by Bandai...
computer game series, Maxwell's demon is referenced in the name of a monster in the first quadrology and as a sword type weapon in its sequel trilogy. - The theory is also referenced in 2003 video-game Max Payne 2, in the form of an in-game cartoon show, the chief villain of which is named "Maxwell's Demon", a creature said to have been created by 'Doctor Entropy' and with the goal of turning the world into a 'dreaded closed system'.
- In the 2007 computer game Neverwinter Nights 2: Mask of the BetrayerNeverwinter Nights 2: Mask of the BetrayerNeverwinter Nights 2: Mask of the Betrayer is a computer role-playing game developed by Obsidian Entertainment and published by Atari. It is an expansion pack for Neverwinter Nights 2. It was released in Autumn 2007 for the PC in North America, Europe, and Australia...
, the player encounters a puzzle in which he controls a trapdoor between two cages containing a mixed population of elemental creatures of fire and ice (mephitMephitIn the fictional world of the Dungeons & Dragons fantasy role-playing game, mephits are extraplanar creatures similar to imps.-Publication history:...
s, which roughly resemble the classical image of the "demon", the point of the puzzle being to separate them despite their tendency to mingle, in essence putting the player in the role of Maxwell's Demon. - In the the online fantasy card game Elements, Maxwell's Demon appears as an entropy-elemental creature card. It is depicted as a red gargoyle-esque beast, with bat wings, and what appears to be a mohican, or a crest on its head. It has the ability 'Paradox', which instantly destroys the target creature, if its attack points are higher than its defence.
Citing Maxwell's Demon, mathematicians philosophized about the actions of an escaped criminal in the American television program Numb3rs
NUMB3RS
Numb3rs is an American television drama which premiered on CBS on January 23, 2005, and concluded on March 12, 2010. The series was created by Nicolas Falacci and Cheryl Heuton, and follows FBI Special Agent Don Eppes and his mathematical genius brother, Charlie Eppes , who helps Don solve crimes...
. The episode, titled "Arrow of Time", was episode 11 of season 5, and originally aired on January 9, 2009.
A Mac Hall
Mac Hall
Mac Hall is a webcomic which was created through a bet between the creator Ian McConville and a friend who claimed he "couldn't make a comic like Penny Arcade". After the fifteenth comic, McConville was joined by Matt Boyd who began to write the comic.Mac Hall follows the exploits of a group of...
comic depicts the character Matt hallucinating a demon named Maxwell who lives in the air conditioner replacing hot air molecules with cool ones. He claims to refute the second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
. The demon's work in progress can be seen in a lighter note in an Abstruse Goose comic.
Maxwell's Demon was a vital element in the plot of the anime series El Cazador de la Bruja
El Cazador de la Bruja
, is an anime television series directed by Kōichi Mashimo and animated by Bee Train studio. It is a spiritual successor of Noir and Madlax and the final installment of Bee Train's "girls-with-guns" trilogy. The series was aired on TV Tokyo from April to September in 2007...
. Scientists recreated what was believed to be an extinct breed of humans capable of interacting with Maxwell's Demon and branded them the name of witches. The deuteragonist of the series, Ellis, was one such witch.
James K. Galbraith's
James K. Galbraith
James Kenneth Galbraith is an American economist who writes frequently for mainstream and liberal publications on economic topics. He is currently a professor at the Lyndon B. Johnson School of Public Affairs and at the Department of Government, University of Texas at Austin. He is also a Senior...
book The Predator State: How Conservatives Abandoned the Free Market and Why Liberals Should Too describes the market as "a disembodied decision maker — a Maxwell's Demon — that, somehow, and without effort, balances and reflects the preferences of everyone participating in economic decisions... It can be these things precisely because it is nothing at all." (Galbraith 19-20)
UK drum and bass producer John B titled a song on his Visions album "Maxwell's Demon".
See also
- Chance and NecessityChance and NecessityChance and Necessity is a 1970 book by Jacques Monod, interpreting the processes of evolution to show that life is only the result of natural processes by "pure chance". It has been described as a "manifesto of materialist biology in the most reductivist sense"...
- CatalysisCatalysisCatalysis is the change in rate of a chemical reaction due to the participation of a substance called a catalyst. Unlike other reagents that participate in the chemical reaction, a catalyst is not consumed by the reaction itself. A catalyst may participate in multiple chemical transformations....
- DispersionDispersionDispersion may refer to:In physics:*The dependence of wave velocity on frequency or wavelength:**Dispersion , for light waves**Dispersion **Acoustic dispersion, for sound waves...
- EvaporationEvaporationEvaporation is a type of vaporization of a liquid that occurs only on the surface of a liquid. The other type of vaporization is boiling, which, instead, occurs on the entire mass of the liquid....
- Gibbs paradoxGibbs paradoxIn statistical mechanics, a semi-classical derivation of the entropy that doesn't take into account the indistinguishability of particles, yields an expression for the entropy which is not extensive...
- Hall effectHall effectThe Hall effect is the production of a voltage difference across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current...
- Heisenberg's Uncertainty Principle
- Joule–Thomson effectJoule–Thomson effectIn thermodynamics, the Joule–Thomson effect or Joule–Kelvin effect or Kelvin–Joule effect describes the temperature change of a gas or liquid when it is forced through a valve or porous plug while kept insulated so that no heat is exchanged with the environment. This procedure is called a...
- Laplace's demonLaplace's demonIn the history of science, Laplace's demon was the first published articulation of causal or scientific determinism by Pierre-Simon Laplace in 1814...
- Laws of thermodynamicsLaws of thermodynamicsThe four laws of thermodynamics summarize its most important facts. They define fundamental physical quantities, such as temperature, energy, and entropy, in order to describe thermodynamic systems. They also describe the transfer of energy as heat and work in thermodynamic processes...
- Mass spectrometryMass spectrometryMass spectrometry is an analytical technique that measures the mass-to-charge ratio of charged particles.It is used for determining masses of particles, for determining the elemental composition of a sample or molecule, and for elucidating the chemical structures of molecules, such as peptides and...
- Photoelectric effectPhotoelectric effectIn the photoelectric effect, electrons are emitted from matter as a consequence of their absorption of energy from electromagnetic radiation of very short wavelength, such as visible or ultraviolet light. Electrons emitted in this manner may be referred to as photoelectrons...
- Quantum tunnellingQuantum tunnellingQuantum tunnelling refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the sun, and has important...
- Schrödinger's catSchrödinger's catSchrödinger's cat is a thought experiment, usually described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that might be...
- Thermionic emissionThermionic emissionThermionic emission is the heat-induced flow of charge carriers from a surface or over a potential-energy barrier. This occurs because the thermal energy given to the carrier overcomes the binding potential, also known as work function of the metal. The charge carriers can be electrons or ions, and...
External links
- Maxwell's Demon by Salman Khan
- Bennett, C.H. (1987) "Demons, Engines and the Second Law", Scientific AmericanScientific AmericanScientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...
, November, pp108-116, pp148-150, Contents - an anthology and comprehensive bibliography of academic papers pertaining to Maxwell's demon and related topics. Chapter 1 (PDF) provides a historical overview of the demon's origin and solutions to the paradox. - Maroney, O. J. E. (2009) ""Information Processing and Thermodynamic Entropy" The Stanford Encyclopedia of Philosophy (Autumn 2009 Edition), reprinted (2001) New York: Dover, ISBN 0-486-41735-2
- Raizen, Mark G. (2011) "Demons, Entropy, and the Quest for Absolute Zero", Scientific AmericanScientific AmericanScientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...
, March, pp54-59 - Splasho (2008) - Historical development of Maxwell's demon
- Reaney, Patricia. "Scientists build nanomachine", Reuters, February 1, 2007
- Rubi, J Miguel, "Does Nature Break the Second Law of Thermodynamics?"; Scientific American, October 2008 :
- Weiss, Peter. "Breaking the Law - Can quantum mechanics + thermodynamics = perpetual motion?", Science News, October 7, 2000