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Microscopic Reversibility and Macroscopic Irreversibility: From the Viewpoint of Algorithmic Randomness

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Abstract

The emergence of deterministic and irreversible macroscopic behavior from deterministic and reversible microscopic dynamics is understood as a result of the law of large numbers. In this paper, we prove on the basis of the theory of algorithmic randomness that Martin-Löf random initial microstates satisfy an irreversible macroscopic law in the Kac infinite chain model. We find that the time-reversed state of a random state is not random as well as it violates the macroscopic law.

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Acknowledgements

The authors thank Naoto Shiraishi and Takahiro Sagawa for their useful comments. The present work was supported by JSPS KAKENHI Grant Number JP17H01148.

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Authors and Affiliations

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

    Ken Hiura & Shin-ichi Sasa

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  1. Ken Hiura
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  2. Shin-ichi Sasa
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Correspondence to Ken Hiura.

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Communicated by Hal Tasaki.

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Hiura, K., Sasa, Si. Microscopic Reversibility and Macroscopic Irreversibility: From the Viewpoint of Algorithmic Randomness. J Stat Phys 177, 727–751 (2019). https://doi.org/10.1007/s10955-019-02387-0

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  • DOI: https://doi.org/10.1007/s10955-019-02387-0

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