  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.
