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.
"Entropy production in nonlinear recombination models." Bernoulli 24 (4B) 3246 - 3282, November 2018. https://doi.org/10.3150/17-BEJ959