# What is a Maxwellian Demon?

In 1871, James Clerk Maxwell (Scottish physicist, biography at St Andrews) 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 hey presto, we've redistributed 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's an excellent demonstration of entropy, how it is related to (a) the fraction of energy that's 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's balanced by at least as big an increase somewhere else).

So why wouldn't 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, and on the atomic and molecular scale you cannot ignore the quantum mechanical nature of the world. For instance, to be able to see the molecules the "demon" would have to absorb whole photons at a time, and any detailed version of the thought experiment will run into the uncertainty principle and the fact that an interacting "demon" will acquire the same temperature as the rest of the system.

The link between thermodynamics and quantum physics is even stronger: macroscopic entropy can only be computed correctly from the cumulative contributions from microscopic states if these are described quantum mechanically.

Information theory is about the concept of entropy abstracted away from physical systems, and applied to any context that deals with knowledge about the state of a system (signal processing, communication, data compression, encryption &c.). In fact, Shannon originally referred to information as "entropy" (with a minus sign). In recent times, there have been interesting developments in applying the ideas of information theory back to physics, notably in dynamical systems theory, aka chaos.

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 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 exciting new field of nanotechnology.

So Maxwell's demon is an icon for our times, sitting at the crossroads of information and the physical universe.

Updated 97-10-17
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