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

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.

12 pages, 12 figures

References in corpus (5)

• Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations
• Autonomous Brownian gyrators: a study on gyrating characteristics
• Nonlinear diffusion from Einstein's master equation
• Ehrenfest urn model with interaction
• Phase Transitions in Ehrenfest Urns Model with Interactions: Coexistence of uniform and non-uniform states

Cited by in corpus (3)

• Theory of Non-equilibrium Asymptotic State Thermodynamics: Interacting Ehrenfest Urn Ring as an Example
• Non-equilibrium Dynamics and Phase Transitions in Potts model and Interacting Ehrenfest urn model
• Coexistence of distinct nonuniform nonequilibrium steady states in Ehrenfest multiurn model on a ring