Explicit Time-Dependent Entropy Production Expressions: Fractional and Fractal Pesin Relations

Abstract

In this contribution, we present for the first time, explicit expressions for time-dependent entropy production, in the classical context. Here, we pursue the understanding of the time dependence of entropy by the approach of nonlocal fractional derivatives and also with local deformed derivatives. We claim that the entropy production depends on the dynamics and the geometry of the complex system considered. Some closed expressions for the entropy growth rate were obtained. We also give a possible explanation for the generalized Pesin relations here obtained, by considering the connection between the fractal geometry of phase-space with the types of particles interactions.

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Correspondence to José Weberszpil.

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Sotolongo-Costa, O., Weberszpil, J. Explicit Time-Dependent Entropy Production Expressions: Fractional and Fractal Pesin Relations. Braz J Phys (2021). https://doi.org/10.1007/s13538-021-00889-5

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Keywords

  • Time-dependent entropy production
  • Generalized Pesin relations
  • Deformed derivatives
  • Fractional calculus
  • Fractals and multifractals
  • Kolmogorov–Sinai entropy