Phase Transitions in Ehrenfest Urns Model with Interactions: Coexistence of uniform and non-uniform states

Abstract

A model based on the classic non-interacting Ehrenfest urn model with two-urns is generalized to $M$ urns with the introduction of interactions for particles within the same urn. As the inter-particle interaction strength is varied, phases of different levels of non-uniformity emerge and their stabilities are calculated analytically. In particular, coexistence of locally stable uniform and non-uniform phases connected by first-order transition occurs. The phase transition threshold and energy barrier can be derived exactly together with the phase diagram obtained analytically. These analytic results are further confirmed by Monte Carlo simulations.

arXiv comment23 pages, 7 figures

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Cited by in corpus (5)

• Deterministic reversible model of non-equilibrium phase transitions and stochastic counterpart
• Non-equilibrium thermodynamics and Phase transition of Ehrenfest urns with interactions
• 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