Maxwells Demon

"Maxwell's Demon" is a thought experiment proposed to confound those who believe in the Second Law of Thermodynamics.

A small (imaginary) being sits by a trap door between two boxes. When the demon sees a high-energy molecule approach the door from the left, it lets the molecule through. When the demon sees a low energy molecule approach the door from the right, it lets the molecule through. For the mere peanuts you have to pay this tiny demon, you can get hot gas from cold gas, and limitless amounts of free energy.

There's no good reason that this can't work, provided that you have something more realistic than a demon to work the trapdoor. Information theorists attempted to salvage the Second Law of Thermodynamics by asserting that the demon would need to measure the molecules, or to remember their positions, etc., and that this act of measuring, remembering, or calculating could not be achieved except by putting forth some physical system, such as a brain, which wastes energy and increases entropy. So they decided that Maxwell's demon could not actually decrease entropy, and could not breach the Second Law of Thermodynamics.

They were and are, however, wrong. Imagine a demon which opens and closes the partition purely at random, and just so happens to do it at all the right times. The chances against this are incredible, but it could happen. The Second "Law" of Thermodynamics is not at all like the Law of Conservation of Energy (or momentum, or whatnot), because those laws cannot be breached in the long term at all, no matter what (so long as they take the uncertainty principle into consideration). The "laws" of Thermodynamics can be breached, even if the probability of such a thing ever happening is incredibly small.