\(H\)-theorem for a linear kinetic theory (Q1203176)

A strong H-theorem is proved for the approximate linear kinetic theory of Blawzdziewicz and Cichocki, obtained by truncating a transformed hierarchy of evolution equations. For an ith truncation we define an entropy functional that is strictly increasing in time, unless the ith reduced distribution function depends on position coordinates only. It also follows that the only stationary solution of the linear kinetic theory is the equilibrium solution. In addition, we show that the usual symmetry properties of equilibrium time correlation functions are preserved by the approximate kinetic theory under consideration.