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Conservation of local equilibrium for attractive particle systems on $$Z^ d$$. (English) Zbl 0798.60085
It is generally expected, that in the hydrodynamic limit local equilibrium holds, i.e. at each time in microscopic neighbourhoods of each macroscopic point the system is approximately in equilibrium. This local equilibrium is characterized by macroscopic parameters depending on time and space, which evolve according to a partial differential equation, the hydrodynamic or Euler equation. In this second paper conservation of local equilibrium is proved for attractive particle systems with one macroscopic equilibrium parameter, the density, if a law of large numbers holds for the density field and under regularity assumptions on the hydrodynamic equation. This theorem is applied to zero range and symmetric simple exclusion processes. The above announced paper is a predecessor, which treats the asymmetric zero range process for special initial profiles with more specific methods.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory
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