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

Original language | English |
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Number of pages | 1 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 67 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2003 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Physics and Astronomy(all)

### Cite this

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**Poincaré cycle of a multibox Ehrenfest urn model with directed transport.** / Kao, Yee Mou; Luan, Pi Gang.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Poincaré cycle of a multibox Ehrenfest urn model with directed transport

AU - Kao, Yee Mou

AU - Luan, Pi Gang

PY - 2003/1/1

Y1 - 2003/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85037246865&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85037246865&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.67.031101

DO - 10.1103/PhysRevE.67.031101

M3 - Article

AN - SCOPUS:85037246865

VL - 67

JO - Physical review. E

JF - Physical review. E

SN - 1539-3755

IS - 3

ER -