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Macroscopic Stability of Time Evolution of Gibbs Measures

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Abstract

We introduce two properties, macroscopic mixing and transitive mixing, to represent the macroscopic stability of time evolution of Gibbs measures. We claim that these are fundamental properties of macroscopic systems that exhibit relaxation to an equilibrium state. As an illustration, we show that a simple mechanical system on a lattice possesses these two properties.

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Acknowledgements

R.L. is supported by the ANR-15-CE40-0020-01 grant LSD and benefited from and invitation fellowship from the JSPS. S. S. is supported by JSPS KAKENHI (Grant Nos. 17H01148, 19H05795, and 20K20425).

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Authors and Affiliations

  1. Université de Paris Cité, Laboratoire de Probabilités, Statistiques et Modélisation, UMR 8001, 75205, Paris, France

    Raphaël Lefevere

  2. Department of Physics, Kyoto University, Kyoto, 606-8502, Japan

    Shin-ichi Sasa

Authors
  1. Raphaël Lefevere
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  2. Shin-ichi Sasa
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Correspondence to Raphaël Lefevere.

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Communicated by Christian Maes.

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Lefevere, R., Sasa, Si. Macroscopic Stability of Time Evolution of Gibbs Measures. J Stat Phys 188, 13 (2022). https://doi.org/10.1007/s10955-022-02943-1

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  • DOI: https://doi.org/10.1007/s10955-022-02943-1

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