Equivalence of ensembles for two-species zero-range invariant measures

TL;DR

This paper investigates the equivalence of ensembles in two-species zero-range processes with unbounded local states, analyzing phase transitions and convergence properties related to condensation phenomena.

Contribution

It establishes ensemble equivalence via relative entropy and derives the phase diagram for condensation in two-species zero-range processes.

Findings

Phase diagram for condensation transition identified.

Convergence properties of Gibbs free energy analyzed.

Large deviations and local limit theorems applied.

Abstract

We study the equivalence of ensembles for stationary measures of interacting particle systems with two conserved quantities and unbounded local state space. The main motivation is a condensation transition in the zero-range process which has recently attracted attention. Establishing the equivalence of ensembles via convergence in specific relative entropy, we derive the phase diagram for the condensation transition, which can be understood in terms of the domain of grand-canonical measures. Of particular interest, also from a mathematical point of view, are the convergence properties of the Gibbs free energy on the boundary of that domain, involving large deviations and multivariate local limit theorems of subexponential distributions.