Ehrenfest urn revisited: playing the game on a realistic fluid model

Scalas, Enrico, Martin, Edgar and Germano, Guido (2007) Ehrenfest urn revisited: playing the game on a realistic fluid model. Physical Review E, 76. 011104(1)-011104(6). ISSN 1539-3755

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The Ehrenfest urn process, also known as the dogs and fleas model, is realistically simulated by molecular dynamics of the Lennard-Jones fluid. The key variable is Delta z, i.e. the absolute value of the difference between the number of particles in one half of the simulation box and in the other half. This is a pure-jump stochastic process induced, under coarse graining, by the deterministic time evolution of the atomic coordinates. We discuss the Markov hypothesis by analyzing the statistical properties of the jumps and of the waiting times between jumps. In the limit of a vanishing integration time-step, the distribution of waiting times becomes closer to an exponential and, therefore, the continuous-time jump stochastic process is Markovian. The random variable Delta z behaves as a Markov chain and, in the gas phase, the observed transition probabilities follow the predictions of the Ehrenfest theory.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Q Science > QC Physics > QC0170 Atomic physics. Constitution and properties of matter Including molecular physics, relativity, quantum theory, and solid state physics
Depositing User: Enrico Scalas
Date Deposited: 29 Sep 2014 10:55
Last Modified: 03 Jul 2019 01:06

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