Non-equilibrium thermodynamics and Phase transition of Ehrenfest urns with interactions

TL;DR

This paper investigates non-equilibrium phase transitions in interacting Ehrenfest urns arranged in a ring, revealing distinct steady states, phase boundaries, and a generalized thermodynamics law through analytical and numerical methods.

Contribution

It introduces a detailed analysis of phase transitions and steady states in interacting Ehrenfest urns, including a generalized thermodynamics law for non-equilibrium systems.

Findings

Identification of two non-equilibrium steady states (uniform and non-uniform)

Analytical and numerical determination of phase boundaries and fluxes

Derivation of a generalized non-equilibrium thermodynamics law

Abstract

Ehrenfest urns with interaction that are connected in a ring is considered as a paradigm model for non-equilibrium thermodynamics and is shown to exhibit two distinct non-equilibrium steady states (NESS) of uniform and non-uniform particle distributions. As the inter-particle attraction varies, a first order non-equilibrium phase transition occurs between these two NESSs characterized by a coexistence regime. The phase boundaries, the NESS particle distributions near saddle points and the associated particle fluxes, average urn population fractions, and the relaxational dynamics to the NESSs are obtained analytically and verified numerically. A generalized non-equilibrium thermodynamics law is also obtained, which explicitly identifies the heat, work, energy and entropy of the system.