Hydrodynamics of the zero-range process in the condensation regime

TL;DR

This paper extends the hydrodynamic description of the zero-range process to the condensation regime, showing that even without local stationarity, a modified hydrodynamic equation accurately captures the system's coarse-grained dynamics, supported by simulations.

Contribution

It introduces an extended hydrodynamic equation for the zero-range process in the condensation regime, a novel approach beyond standard local stationarity assumptions.

Findings

Hydrodynamic equations can describe condensation regime dynamics.

Monte Carlo simulations support the extended model.

Standard hydrodynamics are insufficient without modifications.

Abstract

We argue that the coarse-grained dynamics of the zero-range process in the condensation regime can be described by an extension of the standard hydrodynamic equation obtained from Eulerian scaling even though the system is not locally stationary. Our result is supported by Monte Carlo simulations.