Contrasts between Equilibrium and Non-equilibrium Steady States: Computer Aided Discoveries in Simple Lattice Gases

A century ago, the foundations of equilibrium statistical mechanics were laid. For a system in equilibrium with a thermal bath, much is understood through the Boltzmann factor, exp{-H[C]/kT}, for the probability of finding the system in any microscopic configuration C. In contrast, apart from some special cases, little is known about the corresponding probabilities, if the same system is in contact with more than one reservoir of energy, so that, even in stationary states, there is a constant energy flux through our system. These non-equilibrium steady states display many surprising properties. In particular, even the simplest generalization of the Ising model offers a wealth of unexpected phenomena. Mostly discovered through Monte Carlo simulations, some of the novel properties are understood while many remain unexplained. A brief review and some recent results will be presented, highlighting the sharp contrasts between the equilibrium Ising system and this non-equilibrium counterpart.