Conservation of Local Equilibrium for Attractive Particle Systems on $Z^d$

Abstract

We prove conservation of local equilibrium for attractive particle systems. Our method applies as well to gradient asymmetric processes with mean drift 0 under diffusive $(N^2)$ rescaling. The hydrodynamical behavior is proved for bounded continuous initial profiles under Euler $(N)$ rescaling and for bounded a.s. continuous profiles under diffusive rescaling. We prove that, for attractive systems, the conservation of local equilibrium follows from a law of large numbers for the density field.