Yang-Lee Theory for a Nonequilibrium Phase Transition

Abstract

To analyze phase transitions in a nonequilibrium system we study its grand canonical partition function as a function of complex fugacity. Real and positive roots of the partition function mark phase transitions. This behavior, first found by Yang and Lee under general conditions for equilibrium systems, can also be applied to nonequilibrium phase transitions. We consider a one-dimensional diffusion model with periodic boundary conditions. Depending on the diffusion rates, we find real and positive roots and can distinguish two regions of analyticity, which can identified with two different phases. In a region of the parameter space both of these phases coexist. The condensation point can be computed with high accuracy.