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.

Semiphenomenological model for gas-liquid phase transitions

“…As shown in Ref. [12], the entropy corresponding to the latter model is of the van der Waals type, and if the gas state no longer maximizes the (modified) entropy, the liquid state is likely to become the new maximum.…”

“…To describe all of this process, one should replace the BGK-Vlasov equation (4) with the Enskog-Vlasov equation (see Refs. [11,12]). …”

“…(4) is the so-called Enskog-Vlasov equation introduced in Refs. [11,12], put on a more rigorous footing in Ref. [13], and used in several papers afterward (e.g., Refs.…”