Super-Ricci flows of metric measure spaces

A time-dependent family of Riemannian manifolds is a super-Ricci flow if $2 Ric + \partial_t g \ge 0.$ This includes all static manifolds of nonnegative Ricci curvature as well as all solutions to the Ricci flow equation. We extend this concept of super-Ricci flows to time-dependent metric measure spaces. In particular, we present characterizations in terms of dynamical convexity of the Boltzmann entropy on the Wasserstein space as well in terms of Wasserstein contraction bounds and gradient estimates. And we prove stability and compactness of super-Ricci flows under mGH-limits.