The second-order dynamic phase transition and Lee--Yang zeros in Eggers urn model

A second-order dynamic phase transition in a non-equilibrium Eggers urn model for the separation of sand is studied. The order parameter, the susceptibility and the stationary probability distribution have been calculated. By applying the Lee--Yang zeros method of equilibrium phase transitions, we study the distributions of the effective partition function zeros and obtain the same result for the model. Thus, the Lee--Yang theory can be applied to a more general non-equilibrium system.