Poincaré cycle of a multibox Ehrenfest urn model with directed transport

Yee Mou Kao, Pi Gang Luan

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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 indicates that the fundamental assumption of statistical mechanics holds in this system.

Original languageEnglish
Pages (from-to)9
Number of pages1
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number3
StatePublished - 2003


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