Abstract
Abstract Starting from a master equation for a physical system consisting of mutually non-interacting Brownian particles in a dilute gas and using the collision model of hard spheres we obtain a coupled system of equations of motion for the Brownian distribution function F (R,V; t) and the (single-particle) distribution function f(r,v;t) of the gas. For these equations, assumed to form a "dynamical system", a "H-Theorem" yields asymptotic Lyapunov stability in the large relative to total (Maxwell) equilibrium ("tendency to equilibrium"). For example we investigate approximately the system influenced initially by a sound field (phenomenological coefficients of the equation for F, Fokker-Planck approximation, BGK model for the f-equation).
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