Molecules Distributed between Two Compartments

A box has two compartments connected by a hole. There are molecules in the left compartment and in the right.

To update the original values of and , generate a pseudorandom number between 0 and 1; if , a molecule is added to the left and one is taken away from the right. If , a molecule is added to the right and one is taken away from the left.

With a large number of molecules on one side and a small number on the other side, the system tends to equilibrium after some steps, with small fluctuations afterward. Clearly the entropy of the system increases, evolving to a more disordered state and giving an "arrow of time", making it possible to distinguish the past from the future. But experimenting with a small number of particles is not enough to distinguish past from future. This is because a system with a large number of molecules has a huge number of microstates, and a small system has just a few.