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Science in China Series A: Mathematics

, Volume 44, Issue 3, pp 280–285 | Cite as

Exponential convergence rate in Boltzmann-Shannon entropy

  • Shaoyi Zhang
  • Yonghua Mao
Article

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.

Keywords

Markov semigroups B-S entropy spectral gap logarithmic Sobolev constant 

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Copyright information

© Science in China Press 2001

Authors and Affiliations

  • Shaoyi Zhang
    • 1
    • 2
  • Yonghua Mao
    • 2
  1. 1.Department of MathematicsHubei Normal UniversityHuangshiChina
  2. 2.Department of MathematicsBeijing Normal UniversityBeijingChina

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