Exponential convergence rate in Boltzmann-Shannon entropy |
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| Authors: | ZHANG Shaoyi MAO Yonghua |
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| Affiliation: | 1. Department of Mathematics, Hubei Normal University, Huangshi 435002, China;Department of Mathematics, Beijing Normal University, Beijing 100875, China Correspondence should be addressed to Zhang Shaoyi
2. Department of Mathematics, Beijing Normal University, Beijing 100875, China |
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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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| Keywords: | Markov semigroups B-S entropy spectral gap logarithmic Sobolev constant |
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