In this paper, we present new estimates for the entropy dissipation of the Landau–Fermi–Dirac equation (with hard or moderately soft potentials) in terms of a weighted relative Fisher information adapted to this equation. Such estimates are used for studying the large time behaviour of the equation, as well as for providing new a priori estimates (in the soft potential case). An important feature of such estimates is that they are uniform with respect to the quantum parameter. Consequently, the same estimations are recovered for the classical limit, that is the Landau equation.

中文翻译：

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关于Landau–Fermi–Dirac方程的熵产生的使用

在本文中，我们根据适应于该方程的加权相对Fisher信息，给出了Landau–Fermi–Dirac方程（具有硬或中度软势）的熵耗散的新估计。这样的估计用于研究方程的长时间行为，以及提供新的先验估计（在软势情况下）。这种估计的一个重要特征是，它们在量子参数方面是一致的。因此，对于经典极限，即Landau方程，恢复了相同的估计。