On a class of Lyapunov functionals of the Boltzmann equation and their generalizations

A family of Lyapunov functionals Lα (generalized entropy functionals) of Boltzmann's collision equation is used to judge the sensitivity of the tendency towards the equilibrium against relevant classes of persistent perturbations of the Boltzmann equation. The embedding of the Boltzmann equation into a hierarchy of BBGKY-type is considered from the stability point of view by means of generalized functionals μLα. The derivation of the Boltzmann equation from the hierarchy by a factorization assumption is restated as optimization problem.