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Irreversibility and typicality: A simple analytical result for the Ehrenfest model

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  • Baldovin, Marco
  • Caprini, Lorenzo
  • Vulpiani, Angelo

Abstract

With the aid of simple analytical computations for the Ehrenfest model, we clarify some basic features of macroscopic irreversibility. The stochastic character of the model allows us to give a non-ambiguous interpretation of the general idea that irreversibility is a typical property: for the vast majority of the realizations of the stochastic process, a single trajectory of a macroscopic observable behaves irreversibly, remaining “very close” to the deterministic evolution of its ensemble average, which can be computed using probability theory. The validity of the above scenario is checked through simple numerical simulations and a rigorous proof of the typicality is provided in the thermodynamic limit.

Suggested Citation

  • Baldovin, Marco & Caprini, Lorenzo & Vulpiani, Angelo, 2019. "Irreversibility and typicality: A simple analytical result for the Ehrenfest model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 422-429.
    • Handle: RePEc:eee:phsmap:v:524:y:2019:i:c:p:422-429
    DOI: 10.1016/j.physa.2019.04.188
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    References listed on IDEAS

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    1. Lanford, Oscar E., 1981. "The hard sphere gas in the Boltzmann-Grad limit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 106(1), pages 70-76.
    2. Cerino, L. & Cecconi, F. & Cencini, M. & Vulpiani, A., 2016. "The role of the number of degrees of freedom and chaos in macroscopic irreversibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 486-497.
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