Discontinuous condensation transition and nonequivalence of ensembles in a zero-range process

TL;DR

This paper investigates a zero-range process with system-size dependent jump rates, revealing a discontinuous condensation transition, ergodicity breaking, and nonequivalence of ensembles, supported by rigorous mathematical results and motivated by granular clustering experiments.

Contribution

It provides the first rigorous analysis of a discontinuous condensation transition and nonequivalence of ensembles in a zero-range process with size-dependent jump rates.

Findings

Discontinuous phase transition identified

Ergodicity breaking and metastability observed

Nonequivalence of ensembles in certain phases

Abstract

We study a zero-range process where the jump rates do not only depend on the local particle configuration, but also on the size of the system. Rigorous results on the equivalence of ensembles are presented, characterizing the occurrence of a condensation transition. In contrast to previous results, the phase transition is discontinuous and the system exhibits ergodicity breaking and metastable phases. This leads to a richer phase diagram, including nonequivalence of ensembles in certain phase regions. The paper is motivated by results from granular clustering, where these features have been observed experimentally.