Entropy and Fisher information in non-convex domains: one chain to rule them all
Authors
Jean-Baptiste Casteras
Marco Flaim
Léonard Monsaingeon
Abstract
We prove that the (square root) Fisher information functional is a strong Wasserstein upper gradient of the entropy on non-convex Riemannian domains. This fills a gap in the literature by allowing one to completely dispense from $λ$-displacement convexity arguments. Along the way we establish a novel quantitative short-time control of the Fisher information along the Neumann heat flow, and establish an exact chain rule under stronger $AC_2$ assumptions typically satisfied by curves of measures obtained as limits of JKO schemes.
