Non-equilibrium ensemble inequivalence and density large deviations in the ABC model

TL;DR

This paper investigates the effects of non-conserving processes on the phase behavior and density fluctuations in the driven ABC model, revealing ensemble inequivalence and novel steady-state features when non-conserving rates are comparable to conserving ones.

Contribution

It provides a detailed analysis of phase diagrams and large deviations in the ABC model under different non-conserving rate regimes, highlighting new phenomena such as moving density profiles and ensemble inequivalence.

Findings

Non-conserving processes alter the phase diagram compared to conserving models.

Non-convexity of the large deviations function G(r) leads to ensemble inequivalence.

Moving density profiles occur when non-conserving rates are comparable to conserving rates.

Abstract

We consider the one-dimensional driven ABC model under particle-conserving and particle-non-conserving processes. Two limiting cases are studied: (a) the rates of the non-conserving processes are vanishingly slow compared with the conserving processes in the thermodynamic limit and (b) the two rates are comparable. For case (a) we provide a detailed analysis of the phase diagram and the large deviations function of the overall density, G(r). The phase diagram of the non-conserving model, derived from G(r), is found to be different from the conserving one. This difference, which stems from the non-convexity of G(r), is analogous to ensemble inequivalence found in equilibrium systems with long-range interactions. An outline of the analysis of case (a) was given in an earlier letter. For case (b) we show that unlike the conserving model, the non-conserving model exhibits a moving density profile in the steady-state with a velocity that remains finite in the thermodynamic limit. Moreover, in contrast with case (a), the critical lines of the conserving and non-conserving models do not coincide. These are new features which are present only when the rates of the conserving and non-conserving processes are comparable. In addition, we analyze G(r) in case (b) using macroscopic fluctuations theory. Much of the derivation presented in this paper is applicable to any driven-diffusive system coupled to an external particle-bath via a slow dynamics.