Equilibrium Fluctuations for Zero-Range-Exclusion Processes

We introduce a Markovian particle system which is a kind of lattice gas on Z consisting of particles carrying energy and whose dynamics is a combination of those of an exclusion process (for particles) and a zero-range process (for energy). It has two conserved quantities, the number of particles and the total energy. The process is reversible relative to certain product probability measures, but of non-gradient type. It is proved that under hydrodynamic scaling the equilibrium fluctuation fields of two conserved quantities converge in law to an infinite dimensional Ornstein–Uhlenbeck process.