Entropy and the Ehrenfest urn model

✍ Scribed by Martin J. Klein

• Publisher: Elsevier Science
• Year: 1956
• Weight: 358 KB
• Volume: 22
• Category: Article
• ISSN: 0031-8914
• DOI: 10.1016/s0031-8914(56)90001-5

✦ Synopsis

This note concerns the entropy of the Ehrenfest urn model. Both Boltzmann and Gibbs entropies are discussed. It is shown that they agree at equilibrium. The Boltzmann entropy shows fluctuations in time while the Gibbs entropy is proved to increase monotonically to its maximum (equilibrium) value. The concepts of equilibrium associated with the two points of view are compared.

II. The urn model and its entropy. The model may be described in the following way. Consider two urns, A and B, and 2R balls, numbered consecu-*)