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5. Exponential convergence rate in Boltzmann-Shannon entropy

Exponential convergence rate in Boltzmann-Shannon entropy

来源 :中国科学：数学英文版 | 被引量 : 0次 | 上传用户：qq1036191963

【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

【作 者】

：

ZHANG Shaoyi 

【机 构】

：

1.DepartmentofMathematics,2.DepartmentofMathematics

【出 处】

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中国科学：数学英文版

【发表日期】

：

2001年3期

【关键词】

：

Markov semigroups B-S 熵 光谱豁开 对数的 Sobolev 常数 Markov semigroups B-S entropy spectr 

【基金项目】

：

国家自然科学基金，the Research Fund for the Doctoral Program of H igher Education，教育部霍英东教育基金

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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

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