Statistical mechanics of Landau damping

TL;DR

This paper explores the statistical mechanics underlying Landau damping, analyzing how solutions to the Vlasov equation approach homogeneous states weakly, while density and energy densities approach strongly, revealing entropy dynamics.

Contribution

It introduces a statistical mechanics perspective on Landau damping using Ehrenfest reduction to connect Vlasov solutions with hydrodynamic entropy growth.

Findings

Weak convergence of distribution functions to homogeneous states

Strong convergence of density and energy densities

Growth of hydrodynamic entropy during damping

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 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 Vlasov equation is reduced to the evolution equations for density and kinetic energy density by means of the Ehrenfest reduction.