摘要
This paper deals with the optimal exponential convergence rate βto 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.
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.
基金
This work was supported in part by the National Natural Science Foundation ofChina (Grant Nos. 19771008, 19971025)
the Research Fund for the Doctoral Program of Higher Education (Grant No. 96002704)
Fok Ying-Tung Youth Foundation.
