Recurrence Times for the Ehrenfest Model
Abstract
There is presented a modified scheme of the Ehrenfest model to elucidate certin paradoxes in thermodynamic theory with a continuous time parameter, which was apparently first suggested by A. J. F. Siegert. In this scheme there are two urns and 2N balls initially divided between them arbitrarily. Each ball acts, independently of all the others, as follows: there is a probability of 1/2 dt + o(dt) that the ball changes urns between t and t + dt, and a probability of 1- (1/2 dt + o(dt) that the ball remains ain place between t and t + dt. Standard reasoning then shows that the total probability of a change by some ball between t and t + dt is Ndt + o(dt). When a transfer occurs, it is readily seen that the probabilities that it is from urn 1 to urn 2 or from urn 2 to urn 1, respectively, depend on the relative number of balls in the two urns exactly as for the originial Ehrenfest model.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 08, 1950
- Accession Number
- AD0422808
Entities
People
- Richard E. Bellman
- Theodore Harris
Organizations
- RAND Corporation