Nonequilibrium stationary states and equilibrium models with long range interactions

It was recently suggested by Blythe and Evans that a properly defined steady state normalization factor can be seen as a partition function of a fictitious statistical ensemble in which the transition rates of the stochastic process play the role of fugacities. In analogy with the Lee-Yang description of phase transition of equilibrium systems, they studied the zeros in the complex plane of the normalization factor in order to find phase transitions in nonequilibrium steady states. We show that like for equilibrium systems, the 'densities' associated with the rates are nondecreasing functions of the rates and therefore one can obtain the location and nature of phase transitions directly from the analytical properties of the 'densities'. We illustrate this phenomenon for the asymmetric exclusion process. We actually show that its normalization factor coincides with an equilibrium partition function of a walk model in which the 'densities' have a simple physical interpretation.