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

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.Comment: 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 200

Energy flux distribution in a two-temperature Ising model

The nonequilibrium steady state of an infinite-range Ising model is studied. The steady state is obtained by dividing the spins into two groups and attaching them to two heat baths generating spin flips at different temperatures. In the thermodynamic limit, the resulting dynamics can be solved exactly, and the probability flow in the phase space can be visualized. We can calculate the steady state fluctuations far from equilibrium and, in particular, we find the exact probability distribution of the energy current in both the high- and low-temperature phase.Comment: 19 pages, 4 figure