Maxwell's demon2

Origin and history of the idea

The thought experiment first appeared in a letter Maxwell wrote to Peter Guthrie Tait on 11 December 1867. It appeared again in a letter toJohn William Strutt in 1870, before it was presented to the public in Maxwell's 1871 book on thermodynamics titled Theory of Heat.^[2]

In his letters and book, Maxwell described the agent opening the door between the chambers as a "finite being."

William Thompson (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.^[3][4]

[edit]Original thought experiment

The second law of thermodynamics ensures (through statistical probability) that two bodies of different temperature, 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:^[5]

... if we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are as essentially finite as our own, would be able to do what is impossible to us. For we have seen that molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower molecules to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics....

Schematic figure of Maxwell's demon

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 molecules 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.

Maxwell's demon1

n 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."^[1] 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.

Origin and history of the idea

The thought experiment first appeared in a letter Maxwell wrote to Peter Guthrie Tait on 11 December 1867. It appeared again in a letter toJohn William Strutt in 1870, before it was presented to the public in Maxwell's 1871 book on thermodynamics titled Theory of Heat.^[2]

In his letters and book, Maxwell described the agent opening the door between the chambers as a "finite being."

William Thompson (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.^[3][4]

[edit]Original thought experiment

The second law of thermodynamics ensures (through statistical probability) that two bodies of different temperature, 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:^[5]

... if we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are as essentially finite as our own, would be able to do what is impossible to us. For we have seen that molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower molecules to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics....

Schematic figure of Maxwell's demon

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 molecules 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.