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

TL;DR

This paper investigates the hydrodynamic limits of interacting particle systems on crystal lattices with periodic realizations, revealing how the lattice structure and realization influence the macroscopic behavior.

Contribution

It derives hydrodynamic limits for exclusion and zero range processes on crystal lattices, accounting for inhomogeneous structures and different periodic realizations.

Findings

Hydrodynamic limits depend on lattice structure and realization.

Entropy method effectively derives limits despite inhomogeneity.

Limit equations vary with different periodic realizations.

Abstract

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.