Ehrenfest urn model with interaction

TL;DR

This paper investigates an interacting Ehrenfest urn model, revealing how particle interactions induce phase transitions and analyzing related dynamical properties to identify transition types and metastability.

Contribution

It introduces an interacting version of the Ehrenfest urn model and analyzes phase transition behaviors, relaxation times, and Poincare cycles, providing new insights into nonequilibrium dynamics.

Findings

Interaction induces first- or second-order phase transitions.

Scaling of Poincare cycles indicates phase transition type.

Duration times reveal metastability during first-order transitions.

Abstract

We studied the Ehrenfest urn model in which particles in the same urn interact with each other. Depending on the nature of interaction, the system undergoes a first-order or second-order phase transition. The relaxation time to the equilibrium state, the Poincare cycles of the equilibrium state and the most far-from-equilibrium state, and the duration time of the states during first-order phase transition are calculated. It was shown that the scaling behavior of the Poincare cycles could be served as an indication to the nature of phase transition, and the ratio of duration time of the states could be a strong evidence of the metastability during first-order phase transition.