Nonreversible stationary measures for exchange processes

Abstract

We consider nonreversible exchange dynamics in $Z^d$ and prove that the stationary, translation invariant measures satisfy the following property: if one of them is a Gibbs measure with a summable potential ${J_R, R \subset Z^d}$, then all of them are convex combinations of Gibbs measures with the same potential, but different chemical potentials $J_{\{0\}}$.