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Microscopic reversibility and macroscopic irreversibility: A lattice gas model

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  • Pérez-Cárdenas, Fernando C.
  • Resca, Lorenzo
  • Pegg, Ian L.

Abstract

We present coarse-grained descriptions and computations of the time evolution of a lattice gas system of indistinguishable particles, whose microscopic laws of motion are exactly reversible, in order to investigate how or what kind of macroscopically irreversible behavior may eventually arise. With increasing coarse-graining and number of particles, relative fluctuations of entropy rapidly decrease and apparently irreversible behavior unfolds. Although that behavior becomes typical in those limits and within a certain range, it is never absolutely irreversible for any individual system with specific initial conditions. Irreversible behavior may arise in various ways. We illustrate one possibility by replacing detailed integer occupation numbers at lattice sites with particle probability densities that evolve diffusively.

Suggested Citation

  • Pérez-Cárdenas, Fernando C. & Resca, Lorenzo & Pegg, Ian L., 2016. "Microscopic reversibility and macroscopic irreversibility: A lattice gas model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 82-92.
    • Handle: RePEc:eee:phsmap:v:457:y:2016:i:c:p:82-92
    DOI: 10.1016/j.physa.2016.03.037
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    References listed on IDEAS

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    1. Lebowitz, Joel L., 1999. "Microscopic origins of irreversible macroscopic behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 516-527.
    2. Lebowitz, Joel L., 1993. "Macroscopic laws, microscopic dynamics, time's arrow and Boltzmann's entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 194(1), pages 1-27.
    3. 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.
    Full references (including those not matched with items on IDEAS)

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