Nonequilibrium phase transition in a non integrable zero-range process

TL;DR

This paper analytically explores a non-equilibrium zero-range process, revealing a first-order phase transition between fluid and condensed phases, characterized by macroscopic site occupation and violation of detailed balance.

Contribution

It provides the first analytical and numerical evidence of a phase transition in a non-integrable zero-range process lacking product measure stationary states.

Findings

Existence of a first-order phase transition between fluid and condensed phases.

Identification of a sudden transition from an imbalanced fluid to a condensed state.

Violation of detailed balance even without external drive.

Abstract

The present work is an endeavour to determine analytically features of the stationary measure of a non-integrable zero-range process, and to investigate the possible existence of phase transitions for such a nonequilibrium model. The rates defining the model do not satisfy the constraints necessary for the stationary measure to be a product measure. Even in the absence of a drive, detailed balance with respect to this measure is violated. Analytical and numerical investigations on the complete graph demonstrate the existence of a first-order phase transition between a fluid phase and a condensed phase, where a single site has macroscopic occupation. The transition is sudden from an imbalanced fluid where both species have densities larger than the critical density, to a critical neutral fluid and an imbalanced condensate.