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

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.

References in corpus (6)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields
• Stationary non-equilibrium properties for a heat conduction model
• Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory
• From normal diffusion to superdiffusion of energy in the evanescent flip noise limit