Long-range correlations and ensemble inequivalence in a generalized ABC model

TL;DR

This paper introduces a generalized ABC model with long-range interactions, revealing ensemble inequivalence and phase diagram differences between density-conserving and nonconserving dynamics, advancing understanding of nonequilibrium steady states.

Contribution

It presents a new generalized ABC model with long-range interactions and analyzes its phase behavior under different ensemble conditions, highlighting ensemble inequivalence.

Findings

Both models exhibit detailed balance with a long-range Hamiltonian.

Distinct phase diagrams are observed for canonical and grand canonical ensembles.

Implications for nonequilibrium states with unequal densities are discussed.

Abstract

A generalization of the ABC model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) density-conserving or (ii) nonconserving dynamics. For equal average densities of the three species, both dynamical models are demonstrated to exhibit detailed balance with respect to a Hamiltonian with long-range interactions. The model is found to exhibit two distinct phase diagrams, corresponding to the canonical (density-conserving) and grand canonical (density nonconserving) ensembles, as expected in long-range interacting systems. The implication of this result to nonequilibrium steady states, such as those of the ABC model with unequal average densities, are briefly discussed.