MACROSCOPIC PROPERTIES OF A STATIONARY NONEQUILIBRIUM DISTRIBUTION FOR A NONGRADIENT INTERACTING PARTICLE SYSTEM

We consider a one dimensional generalized symmetric simple exclusion p rocess where are permitted at most two particles per site. The system is open and at the boundaries a stochastic dynamic is chosen to model two infinite reservoirs of particles with different densities. This si mple model is non gradient. We prove that in the stationary state the particles empirical density field converges to the deterministic solut ion of a non linear elliptic equation as the microscopic size of the s ystem goes to infinity. Fick's law of transport for the expected value of the current in the stationary state is also proven.