Conservative Interacting Particles System with Anomalous Rate of Ergodicity

We analyse certain conservative interacting particle system and establish ergodicity of the system for a family of invariant measures. Furthermore, we show that convergence rate to equilibrium is exponential. This result is of interest because it presents counterexample to the standard assumption of physicists that conservative system implies polynomial rate of convergence. The system in question is stochastic rather than deterministic.