Examples of two point kinetic equations obeying the entropy principle

Abstract

Qualitative properties of solutions of a two point extension of the Boltzmann kinetic equation and of solutions of the Frey–Salmon two point kinetic equation are investigated. Our attention is focussed on: (i) compatibility of the long time behaviour of solutions with equilibrium thermodynamics, (ii) the thermodynamic equation of state implied by the two point kinetic equations, (iii) one point kinetic equations whose solutions approximate well the solutions to the two point kinetic equations for large time, and (iv) transport coefficients implied by the two point kinetic equations.