Scalas, Enrico;
Martin, Edgar;
Germano, Guido;
(2007)
Ehrenfest urn revisited: Playing the game on a realistic fluid model.
Physical Review E
, 76
(1)
, Article 011104. 10.1103/PhysRevE.76.011104.
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Abstract
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 ∆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 the 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 ∆z behaves as a Markov chain and, in the gas phase, the observed transition probabilities follow the predictions of the Ehrenfest theory.
| Type: | Article |
|---|---|
| Title: | Ehrenfest urn revisited: Playing the game on a realistic fluid model |
| Location: | United States |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1103/PhysRevE.76.011104 |
| Publisher version: | https://doi.org/10.1103/physreve.76.011104 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10209718 |
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