Between equilibrium fluctuations and Eulerian scaling: Perturbation of equilibrium for a class of deposition models

Abstract

We investigate propagation of perturbations of equilibrium states for a wide class of 1D interacting particle systems. The class of systems considered incorporates zero range, $K$-exclusion, mysanthropic, `bricklayers' models, and much more. We do not assume attractivity of the interactions. We apply Yau's relative entropy method rather than coupling arguments. The result is \emph{partial extension} of T. Seppäläinen's recent paper. For $0<β<1/5$ fixed, we prove that, rescaling microscopic space and time by $N$, respectively $N^{1+β}$, the macroscopic evolution of perturbations of microscopic order $N^{-β}$ of the equilibrium states is governed by Burgers' equation. The same statement should hold for $0<β<1/2$ as in Seppäläinen's cited paper, but our method does not seem to work for $β\ge1/5$.

30 pages version 2: some typos corrected, some remarks added