# Maxwell's demon

Maxwell's demon

Maxwell's demon is an 1867 thought experiment of James Clerk Maxwell suggesting how the second law of thermodynamics might hypothetically be violated. The description was contained in his Theory of Heat in 1871. As individual gas molecules approach a small hole, his demon quickly opens and shuts it to allow only fast molecules to passed from chamber A into chamber B, and only the slower particles to pass back from chamber B. This causes the the second chamber to warm and the original chamber to cool, even though the chambers are originally at the same temperature. Entropy has thereby decreased, violating the second law of thermodynamics. This idea has provoked debate and theoretical work on the relation between thermodynamics and information theory.

## Quotes

### Theory of Heat (1871)

James Clerk Maxwell
• [T]he Diffusion of Heat ...invariably transfers heat from a hotter body to a colder one, so as to cool the hotter body and warm the colder... This process would go on till all bodies were brought to the same temperature if it were not for certain other processes...
• One of the best established facts in thermodynamics is that it is impossible in a system enclosed in an envelope which permits neither change of volume nor passage of heat, and in which both the temperature and the pressure are every where the same, to produce any inequality of temperature or of pressure without the expenditure of work. This is the second law of thermodynamics, and it is undoubtedly true as long as we can deal with bodies only in mass, and have no power of perceiving or handling the separate molecules of which they are made up.
• But 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.

### The Demon in the Machine by Paul Davies (Sep 7, 2019)

Paul Davies, 6th International FQXi Conference, "Mind Matters: Intelligence and Agency in the Physical World." A source.
• [I]nformation... does enter into physics and has been in physics for a long time, in the most obvious way with Maxwell's demon... [which] is able to use information about the motions of molecules to operate a shutter mechanism and put all the fast-moving ones on the left and the slow-moving ones on the right, thus establishing a temperature difference from which work can be extracted. You can run a heat engine, lift a weight [etc.]
• [T]he demon... is transferring heat from a colder region to a warmer region in apparent defiance of the second law of thermodynamics. "And hold on," you're thinking, "doesn't my refrigerator do that?" Sure... a refrigerator... costs energy to run... but the demon is operating using information instead... The demon... runs without any energy expenditure.
• So in effect, information serves as a fuel, and this leads to the whole concept of information engines. Engines that will run on information power, and... there is an FQXi initiative on this...
• Life was onto this... billions of years ago. Life uses many many nano-molecules which are, in effect, Maxwell demons. Our bodies are full of little Maxwell demons... doing the business of life. These little molecular machines are not quite perfect... but they're coming pretty close to the theoretical limit, in terms of energy expenditure.
• Voltage-gated ion channels are the way in which, even now, you are thinking and paying attention, because the signals that travel between neurons, down the axons, are controlled by the flow of ions across the membranes of the axons... [T]hey are, in effect, little demons that sense the incoming signal and open and close the gates; and the ions flow. ...[T]his is so incredibly energy efficient that ...your brain, which is like a megawatt supercomputer, operates with the energy equivalent of a small light bulb.
• [I]n order to investigate this... [I]f you have a Maxwell demon or something like a Szilard engine in De Sitter space, could you use it, as Maxwell envisaged, to use information to extract energy from De Sitter space and lift a weight or do some sort of useful work? ...[T]he answer would seem to be, only if you can create a region of the De Sitter space that is screened out from that horizon, screened out from that thermal nature. If you put a reflective barrier around the demon, you then have De Sitter space, but with the horizon screened out. ...[T]hat's a problem I'm working on now ...