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

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