A dynamical transition and metastability in a size-dependent zero-range process

TL;DR

This paper rigorously analyzes a size-dependent zero-range process, revealing a dynamical transition and metastability phenomena related to condensation, with implications for understanding finite-size effects in condensing particle systems.

Contribution

It provides the first rigorous characterization of large deviation properties, free energy landscape, and metastable dynamics in a size-dependent zero-range process.

Findings

Identification of a new dynamic transition line within the condensed phase

Characterization of metastable homogeneous and condensed phases

Analysis of timescales governing condensate motion

Abstract

We study a zero-range process with system-size dependent jump rates, which is known to exhibit a discontinuous condensation transition. Metastable homogeneous phases and condensed phases coexist in extended phase regions around the transition, which have been fully characterized in the context of the equivalence and non-equivalence of ensembles. In this communication we report rigorous results on the large deviation properties and the free energy landscape which determine the metastable dynamics of the system. Within the condensed phase region we identify a new dynamic transition line which separates two distinct mechanism of motion of the condensate, and provide a complete discussion of all relevant timescales. Our results are directly related to recent interest in metastable dynamics of condensing particle systems. Our approach applies to more general condensing particle systems, which exhibit the dynamical transition as a finite size effect.