Entropy and curvature of Markov chains on metric spaces

This talk is devoted to the celebrated Peres-Tetali
conjecture, which asserts that any Markov chain exhibiting contraction
in the Wasserstein distance should also exhibit contraction in relative
entropy, by the same amount. I will give a brief historical overview of
this question, describe our main result, and illustrate it with several
applications, including Zero-Range processes, Glauber dynamics, and the
Langevin diffusion in a convex potential.

This is based on joint works with Pietro Caputo and Florentin Münch.