Hydrodynamic limits of interacting particle systems on crystal lattices in periodic realizations

We study the hydrodynamic limits of the simple exclusion processes and the zero range processes on crystal lattices. For a periodic realization of crystal lattice, we derive the hydrodynamic limit for the exclusion processes and the zero range processes, which depends on both the structure of crystal lattice and the periodic realization. Even through the crystal lattices have inhomogeneous local structure, for all periodic realizations, we apply the entropy method to derive the hydrodynamic limits. Also, we discuss how the limit equation depends on the choices of the realizations.