From irreversibility in physics to optimal convergence rates in: 50 years of research in Dauphine: yesterday, today and tomorrow 1968 / 2019

The explanation of irreversibility by L. Boltzmann at the end of the 19th century raised the attention of mathematicians to the notion of entropy, which was later reinvented several times in various areas of science ranging from probability theory to information theory. The issue of quantitative estimates is fundamental for applications: what is the rate of convergence of a solution to an equilibrium, if there is any ? First results on this issue were obtained only quite recently, based on renormalized solutions of kinetic equations, mass transport and hypocoercive methods. Researchers of Dauphine and their collaborators played a central role in this area, at the interface of nonlinear analysis, measure theory and probability theory.