This is a preliminary page for a nice toy model from a talk by Beate Schmittman from Virginia Tech Physics.

The rules are simple. Start with a grid of particles which have equal likelihood of hopping left, right, up, or down. Then identify some positive and some negative charges in a field so that half prefer to jump up, half prefer to jump down. If we make the system periodic, as though the charges crawled around a cylinder or torus, then we have a driven non-equilibrium system. To the right is a system with one up and one down particle moving slowly around the board.