Local H theorem for Enskog and Enskog-Vlasov equations with a modified Enskog factor

TL;DR

This paper proves the local H theorem for the Enskog and Enskog-Vlasov equations with a modified Enskog factor, extending previous global results and strengthening the theoretical understanding of these kinetic equations.

Contribution

The authors establish the local H theorem for the modified Enskog and Enskog-Vlasov equations, providing a stronger theoretical result than previously known.

Findings

Local H theorem holds for the modified Enskog equation

Local H theorem also applies to the Enskog-Vlasov equation

The results extend previous global H theorem to a local context

Abstract

The local H theorem is shown to hold for the Enskog equation with a modified Enskog factor proposed by the authors [Phys. Rev. E 111, 065108 (2025)]. This is a stronger statement than the global one in the same paper and has been obtained along the lines of Mareschal et al. [Phys. Rev. Lett. 52, 1169-1172 (1984)] for the modified (or revised) Enskog equation. Furthermore, it is shown that the local H theorem also holds for the corresponding Enskog-Vlasov equation.