Kinetic Equation of Classical Boltzmann Gases

Abstract

By use of the multiple-time-scale method, the low density expansion is carried to the order of the triple collision integral. The validity of Bogoliubov's assumption that the multiple distribution depends functionally on a single particle distribution is carefully examined. It is found that such an assumption is valid except locally for those particles which have a large separation at a time t and which have their relative velocity so oriented that they were in collision at t = 0. Since this local breakdown is very selective, the triple collision integral which is found in the literature is still correct. As a by-product of the multiple-time-scale method, the rate at which a system approaches the kinetic state is obtained; it is also found that up to the order considered the Maxwellian distribution is the only solution at thermal equilibrium.