Hydrodynamic Limit of One-Dimensional Exclusion Processes with Speed Change

Abstract

Hydrodynamic behavior of one-dimensional homogeneous exclusion processes with speed change on periodic lattices $\mathbb{Z}/N\mathbb{Z}, N = 1,2,3,\ldots$, is studied. For every reversible exclusion process with nearest neighbor jumps and local interactions of gradient type it is shown that under diffusion-type scaling in space and time the empirical density fields of the processes converge to a weak solution of a nonlinear diffusion equation as $N$ goes to infinity. Two classes of examples of exclusion processes as stated are given.