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

  • Ken HiuraEmail author
  • Shin-ichi Sasa
Article
  • 18 Downloads

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.

Keywords

Microscopic reversibility Macroscopic irreversibility Algorithmic randomness Kac model 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsKyoto UniversityKyotoJapan

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