Entropy production in nonlinear recombination models

TL;DR

This paper investigates how nonlinear recombination models approach equilibrium by analyzing entropy production, introducing a general framework, and deriving new entropy inequalities that quantify convergence rates.

Contribution

It provides a tight quantitative estimate for entropy production in nonlinear recombination models within the Reversible Quadratic Systems framework, extending existing entropy inequalities.

Findings

Established a new entropy production estimate for nonlinear recombination models

Generalized Shearer's inequality in the context of entropy

Demonstrated convergence to equilibrium using entropy measures

Abstract

We study the convergence to equilibrium of a class of nonlinear recombination models. In analogy with Boltzmann's H theorem from kinetic theory, and in contrast with previous analysis of these models, convergence is measured in terms of relative entropy. The problem is formulated within a general framework that we refer to as Reversible Quadratic Systems. Our main result is a tight quantitative estimate for the entropy production functional. Along the way we establish some new entropy inequalities generalizing Shearer's and related inequalities.