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Exponential convergence rate in Boltzmann-Shannon entropy

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Abstract

This paper deals with the optimal exponential convergence rate β to the equilibrium state in Boltzmann-Shannon entropy for general Markov semigroups. We prove a variational formula of β, and then discuss the relation among β, spectral gap λ and logarithmic Sobolev constant α, which is read as λ≥β≥α.

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Authors and Affiliations

  1. Department of Mathematics, Hubei Normal University, 435002, Huangshi, China

    Shaoyi Zhang

  2. Department of Mathematics, Beijing Normal University, 100875, Beijing, China

    Shaoyi Zhang & Yonghua Mao

Authors
  1. Shaoyi Zhang
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  2. Yonghua Mao
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Zhang, S., Mao, Y. Exponential convergence rate in Boltzmann-Shannon entropy. Sci. China Ser. A-Math. 44, 280–285 (2001). https://doi.org/10.1007/BF02878707

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  • DOI: https://doi.org/10.1007/BF02878707

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