Non-equilibrium stationary properties of the boundary driven zero-range process with long jumps

TL;DR

This paper studies the non-equilibrium stationary behavior of a zero-range process with long jumps, deriving fundamental properties like the hydrostatic limit, Fick's law, and large deviation principles, revealing deep connections with exclusion processes.

Contribution

It introduces the analysis of zero-range processes with long jumps in non-equilibrium states, establishing new hydrodynamic limits and free energy characterizations.

Findings

Derived the hydrostatic limit for the process

Established Fick's law in the non-equilibrium setting

Computed the large deviation principle for empirical density

Abstract

We consider the zero-range process with long jumps and in contact with infinitely many reservoirs in its non-equilibrium stationary state. We derive the hydrostatic limit and the Fick's law, which are a consequence of a relationship between the exclusion process and the zero-range process. We also obtain the large deviation principle for the empirical density, i.e. we compute the non-equilibrium free energy.