Hydrodynamic limit for multi-species exclusion processes

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We studied the hydrodynamic limit for multi-species lattice gas model, which is a simplified model for large scale interacting particle systems. The proof of the hydrodynamic limit is divided into three parts. We proved first and second parts, "an estimate of the spectral gap" and "the central limit theorem variance". However third part, "properties of limiting equation", is not proved.We also obtained similar results for "exclusion process with degenerate rates", which has similar properties to multi-species lattice gas model.