通过简化为流体动力学对朗道阻尼的热力学解释。

Thermodynamic Explanation of Landau Damping by Reduction to Hydrodynamics.

作者信息

Pavelka Michal, Klika Václav, Grmela Miroslav

机构信息

Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague, Czech Republic.

Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic.

出版信息

Entropy (Basel). 2018 Jun 12;20(6):457. doi: 10.3390/e20060457.

DOI:10.3390/e20060457

PMID:33265547

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7512976/

Abstract

Landau damping is the tendency of solutions to the Vlasov equation towards spatially homogeneous distribution functions. The distribution functions, however, approach the spatially homogeneous manifold only weakly, and Boltzmann entropy is not changed by the Vlasov equation. On the other hand, density and kinetic energy density, which are integrals of the distribution function, approach spatially homogeneous states strongly, which is accompanied by growth of the hydrodynamic entropy. Such a behavior can be seen when the Vlasov equation is reduced to the evolution equations for density and kinetic energy density by means of the Ehrenfest reduction.

摘要

朗道阻尼是指弗拉索夫方程的解趋向于空间均匀分布函数的趋势。然而，分布函数只是微弱地趋近于空间均匀流形，并且玻尔兹曼熵不会因弗拉索夫方程而改变。另一方面，作为分布函数积分的密度和动能密度则强烈地趋近于空间均匀状态，这伴随着流体动力学熵的增加。当通过埃伦费斯特约化将弗拉索夫方程简化为密度和动能密度的演化方程时，就可以看到这种行为。