  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.
