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Entropy 2018, 20(6), 457; https://doi.org/10.3390/e20060457

Thermodynamic Explanation of Landau Damping by Reduction to Hydrodynamics

1
Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague, Czech Republic
2
Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic
3
École Polytechnique de Montréal, C.P.6079 suc. Centre-ville, Montréal, QC H3C 3A7, Canada
*
Author to whom correspondence should be addressed.
Received: 11 April 2018 / Revised: 3 June 2018 / Accepted: 8 June 2018 / Published: 12 June 2018
(This article belongs to the Special Issue Mesoscopic Thermodynamics and Dynamics)
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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. View Full-Text
Keywords: Landau damping; entropy; non-equilibrium thermodynamics; Ehrenfest reduction Landau damping; entropy; non-equilibrium thermodynamics; Ehrenfest reduction
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Pavelka, M.; Klika, V.; Grmela, M. Thermodynamic Explanation of Landau Damping by Reduction to Hydrodynamics. Entropy 2018, 20, 457.

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