Maxwell's demon

In 1871, the Scottish physicist James Clerk Maxwell proposed a thought experiment. A wall separates two compartments filled with gas. A little "demon" sits by a tiny trapdoor in the wall. It looks at oncoming gas molecules, and depending on their speeds it opens or closes the trapdoor. The object of the game is to eventually collect all the molecules faster than average on one side, and the slower ones on the other side.

We end up with a hot, high pressure gas on one side, and a cold, low pressure gas on the other. Conservation of energy is not violated, but we have managed to redistribute the random kinetic energy of the molecules (heat) in such a way that energy can now be extracted from the system (it can drive a gas turbine, say).

Maxwell didn't call the demon in the story after himself of course. Norbert Wiener refers to it as "the Maxwell demon", the phrase "Maxwell's demon" is also often heard.

It is an excellent demonstration of entropy, how it is related to

(a) the fraction of energy that is not available to do useful work, and

(b) the amount of information we lack about the detailed state of the system.

In Maxwell's thought experiment, the demon manages to decrease the entropy, in other words it increases the amount of energy available by increasing its knowledge about the motion of all the molecules.

Thermodynamics says this is impossible, you can only increase entropy (or rather, you can decrease it at one place as long as that is balanced by at least as big an increase somewhere else).

So why would not a setup like Maxwell's demon work? Well, any real "demon" that does this would not be a disembodied spirit receiving its information telepathically. To acquire information about the world you must be in physical interaction with it. In determining what side of the gate a molecule must be on, the demon must store information about the state of the molecule. Eventually, the demon will run out of information storage space and must begin to erase the information that has been previously gathered. Erasing information is a thermodynamically irreversible process that increases the entropy of a system. Maxwell's demon therefore reveals a deep connection between thermodynamics and information theory.

Real-life versions of Maxwellian demons (with their entropy lowering effects of course duly balanced by increase of entropy elsewhere) actually occur in living systems, such as the ion channels and pumps that make our nervous systems work, including our minds. Molecular-sized mechanisms are no longer found only in biology however, it's also the subject of the emerging field of nanotechnology.

Maxwell's demon plays a not-insignificant role in the book The Crying of Lot 49 by noted author Thomas Pynchon