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

TL;DR

This paper explores the fundamental differences between equilibrium and non-equilibrium steady states in lattice gases, highlighting surprising phenomena and recent discoveries made through computer simulations, especially in simple models like the Ising system.

Contribution

It provides a comparative analysis of equilibrium and non-equilibrium steady states, emphasizing new phenomena in non-equilibrium systems revealed by computer-aided methods.

Findings

Non-equilibrium states exhibit unexpected properties not seen in equilibrium.

Monte Carlo simulations reveal novel phenomena in simple lattice gases.

Some non-equilibrium behaviors are partially understood, others remain unexplained.

Abstract

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.