There is a box that contains two chambers each containing gas molecules at the same temperature.  A demon controls a door between the two chambers.  He opens it if in the right chamber he sees a particle moving fast right to left or if he sees a particle in the left chamber moving slow left to right.  Over time, the left chamber is hot and the right chamber is cold.

The problem is the entropy of the system supposedly didn’t increase — it decreased!

Maxwell presented this scenario in the 1800’s and it took physicists like a hundred years to figure it out.  Supposedly, the amount of entropy in the system increased when the demon “forgets” about each particle that he is tracking.  There is this whole theory of reversible computing where the computation takes no energy but the clearing of registers takes energy and produces entropy.  The demon acts as a irreversible state machine consuming energy and increasing the entropy of the system.  (Not that all this makes sense to me as I have forgotten almost everything I ever knew about thermodynamics).