Maxwell’s demon is a rather fascinating thought experiment. Suppose you have a box filled with gas, divided in two by a wall. On top of the wall sits a demon who can see every approaching gas molecule, and may let a molecule pass at his discretion.
Hot molecules travel faster than cold ones, so if he lets all the hot ones through, he could seemingly pump heat without using any energy.
As it turns out, the cost of computation explains it. The demon is a computer, and computation uses energy.