Abstract
The hydrodynamic limit for the class of lattice gases that are reversible under the Bernoulli measures is studied by estimating the relative entropy of the microscopic state of actual system with respect to a local equilibrium state (the method of H.T. Yau). The model discussed in this article is of non-gradient type and this forces us to introduce the local equilibrium state of second order approximation that is made according to the variational formula (an equivalent of the Green-Kubo formula) for the diffusion coefficient due to S.R.S. Varadhan. The estimation of the relative entropy is carried out by adapting the “gradient replacement” devised by Varadhan for the study of the Ginzburg-Landau model of non-gradient type. Because of the method adopted we do not need tightness argument nor two-block estimate, but do need to assume that the solution of the limiting nonlinear diffusion equation is smooth.
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