Extending Cercignani’s Conjecture Results from Boltzmann to Boltzmann–Fermi–Dirac Equation

IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Thomas Borsoni
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引用次数: 0

Abstract

We establish a connection between the relative Classical entropy and the relative Fermi–Dirac entropy, allowing to transpose, in the context of the Boltzmann or Landau equation, any entropy–entropy production inequality from one case to the other; therefore providing entropy–entropy production inequalities for the Boltzmann–Fermi–Dirac operator, similar to the ones of the Classical Boltzmann operator. We also provide a generalized version of the Csiszár–Kullback–Pinsker inequality to weighted \(L^p\) norms, \(1 \le p \le 2\) and a wide class of entropies.

将塞西尼亚尼猜想的结果从玻尔兹曼扩展到玻尔兹曼-费米-狄拉克方程
我们在相对经典熵和相对费米-狄拉克熵之间建立了联系,从而可以在玻尔兹曼方程或朗道方程的背景下,将任何熵-熵生成不等式从一种情况转置到另一种情况;因此为玻尔兹曼-费米-狄拉克算子提供了熵-熵生成不等式,类似于经典玻尔兹曼算子的熵-熵生成不等式。我们还提供了Csiszár-Kullback-Pinsker不等式的广义版本,它适用于加权\(L^p\)规范、\(1 \le p \le 2\) 和一大类熵。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Statistical Physics
Journal of Statistical Physics 物理-物理:数学物理
CiteScore
3.10
自引率
12.50%
发文量
152
审稿时长
3-6 weeks
期刊介绍: The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.
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