Contrasts between equilibrium and non-equilibrium steady states: Computer aided discoveries in simple lattice gases

DOI10.1016/S0010-4655(00)00022-9zbMATH Open0981.82013arXivcond-mat/9906376MaRDI QIDQ1568561

R. J. Astalos, R. K. P. Zia, B. Schmittmann, Leah B. Shaw

Publication date: 27 March 2002

Published in: Computer Physics Communications (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/cond-mat/9906376

zbMATH Keywords

Monte Carlo phase transitions nonequilibrium steady states lattice gas driven diffusive systems

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to statistical mechanics (82-02) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26)