Generalized kinetic theory

Abstract

Abstract Up to the early 1970s, a ‘kinetic approach’ to the time-dependent properties of fluids was synonymous with a framework based on statistical mechanics in which a central role is played by those dynamical events referred to as uncorrelated binary collisions. Although the details of these collisional events depend on the specific form of the interatomic potential, in most cases the relevant effects are due to the harsh repulsion prevailing at small separations, often modelled as a ‘hard sphere’ interaction. As a consequence, a collision may usually be considered as an event strongly localized both in space and time. Because of this character, it seems reasonable to assume that two subsequent collisions are mutually uncorrelated. This assumption is actually one of the cornerstones of the traditional kinetic frameworks since their invention by Boltzmann more than a century ago. If we explore at a deeper qualitative level the physical content of the uncorrelated-collisions assumption, we arrive at the conclusion that this ansatz is indeed justified for dilute fluids, where the collisional events are comparatively rare so that, in a sense, a particle has available an amount of space and time sufficient to ‘forget’ a collision before the occurrence of another one.