CONSERVATION OF LOCAL EQUILIBRIUM FOR ATTRACTIVE PARTICLE-SYSTEMS ON Z(D)

We prove conservation of local equilibrium for attractive particle sys tems. Our method applies as well to gradient asymmetric processes with mean drift 0 under diffusive (N-2) rescaling. The hydrodynamical beha vior is proved for bounded continuous initial profiles under Euler (N) rescaling and for bounded a.s. continuous profiles under diffusive re scaling. We prove that, for attractive systems, the conservation of lo cal equilibrium follows from a law of large numbers for the density fi eld.