Non-equilibrium Stationary Properties of the Boundary Driven Zero-Range Process with Long Jumps

We consider the zero-range process with long jumps and in contact with infinitely extended reservoirs in its non-equilibrium stationary state. We derive the hydrostatic limit and the Fick's law, which are a consequence of a static 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.

Automated summary

This paper investigates the non-equilibrium stationary state of the zero-range process with long jumps and in contact with infinitely extended reservoirs. The hydrostatic limit, Fick's law, and the large deviation principle for the empirical density are derived.