Pairwise balance and invariant measures for generalized exclusion processes

Abstract

We characterize the steady state of a driven diffusive lattice gas in which each site holds several particles, and the dynamics is activated and asymmetric. Using a quantum Hamiltonian formalism, we show that for arbitrary transition rates the model has product invariant measure. In the steady state, a pairwise balance condition is shown to hold. Configurations n" and n' leading respectively into and out of a given configuration n are matched in pairs so that the flux of transitions from n" to n is equal to the flux from n to n'. Pairwise balance is more general than the condition of detailed balance and holds in the non-equilibrium steady state of a number of stochastic models.