Poincare cycle of an Ehrenfest multiurn model in a one-dimensional ring

Abstract

We study an Ehrenfest multiurn model of a one-dimensional ring, generalizing the directed transport in the previous model to arbitrary transports. We analytically study the evolution of the system and calculate the Poincare cycle for given transport probabilities. The result shows that the average number of balls in an urn evolves according to the transport probability, but the Poincare cycle is only related to the initial configuration.