Maxwell's Demon - violating the entropy

Maxwell's demon is an imaginary creature created by James Clerk Maxwell in 1867. It is a thought experiment meant to raise questions about the possibility of violating the second law of thermodynamics.

Suppose there is a room filled with a gas at some temperature. This means that the average speed of the molecules is a certain amount depending on the temperature. Some of the molecules will be going faster than average and some will be going slower than average. Suppose that a partition is placed across the middle of the room separating the two sides into left and right. Both sides of the room are now filled with the gas at the same temperature.

Maxwell imagined a molecule sized trap door in the partition with his minuscule creature (the demon) poised at the door who is observing the molecules (look at the picture above). When a faster than average molecule approaches the door he makes certain that it ends up on the left side (by opening the tiny door if it's coming from the right) and when a slower than average molecule approaches the door he makes sure that it ends up on the right side.

So after these operations he ends up with a room in which all the faster than average gas molecules are in the left side and all the slower than average ones are in the right side. So the room is hot on the left and cold on the right. Then one can use this separation of temperature to run a heat engine by allowing the heat to flow from the hot side to the cold side.

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.