Poincaré cycle of a multibox Ehrenfest urn model with directed transport

Abstract

We propose a generalized Ehrenfest urn model of many urns arranged periodically along a circle. The evolution of the urn model system is governed by a directed stochastic operation. Method for solving an $N$-ball, $M$-urn problem of this model is presented. The evolution of the system is studied in detail. We find that the average number of balls in a certain urn oscillates several times before it reaches a stationary value. This behavior seems to be a peculiar feature of this directed urn model. We also calculate the Poincaré cycle, i.e., the average time interval required for the system to return to its initial configuration. The result can be easily understood by counting the total number of all possible microstates of the system.

10 pages revtex file with 7 eps figures

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Cited by in corpus (8)

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• Drifting diffusion on a circle as continuous limit of a multiurn Ehrenfest model
• Non-equilibrium thermodynamics and Phase transition of Ehrenfest urns with interactions
• The ideal gas as an urn model: derivation of the entropy formula
• A probabilistic model for the equilibration of an ideal gas