Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states

Abstract

One of the key features of non-equilibrium steady states (NESS) is the presence of nontrivial probability currents. We propose a general classification of NESS in which these currents play a central distinguishing role. As a corollary, we specify the transformations of the dynamic transition rates which leave a given NESS invariant. The formalism is most transparent within a continuous time master equation framework since it allows for a general graph-theoretical representation of the NESS. We discuss the consequences of these transformations for entropy production, present several simple examples, and explore some generalizations, to discrete time and continuous variables.

39 pages, 5 figures. Invited article for JSTAT Special Issue on 'Principles of Dynamics of Nonequilibrium Systems', held at the Newton Institute, Cambridge, UK, in 2006