Ergodicity in infinite Hamiltonian systems with conservative noise

Summary. We study the stationary measures of an infinite Hamiltonian system of interacting particles in ℝ ³ subject to a stochastic local perturbation conserving energy and momentum. We prove that the translation invariant measures that are stationary for the deterministic Hamiltonian dynamics, reversible for the stochastic dynamics, and with finite entropy density, are convex combination of “Gibbs” states. This result implies hydrodynamic behavior for the systems under consideration. Received: 17 December 1994/In revised form: 12 April 1996