Entropy dissipation inequality for general binary collision models

TL;DR

This paper introduces a new entropy inequality framework for non-reversible binary collision models, extending the H-Theorem to broader classes of kinetic equations and Markov chains.

Contribution

It formulates a two-particle factorization condition enabling entropy inequalities for non-reversible collision kernels, with examples and a variational approach for Markov chains.

Findings

Established an entropy dissipation inequality for non-reversible collision models.

Provided examples of models satisfying the new condition.

Extended the entropy framework to non-reversible Markov chains.

Abstract

We introduce a ``two-particle factorization'' condition which allows us to formulate the homogeneous Boltzmann equation for non-reversible collision kernels in terms of an entropy inequality. This formulation yields an H-Theorem. We provide some examples of non-reversible binary collision models with a concentration/dispersion mechanism, as in opinion dynamics, which satisfy this condition. As a preliminary step, we also provide an analogous variational formulation of non-reversible continuous time Markov chains, expressed in terms of an entropy dissipation inequality.