Open Collections

When Otto meets Newton and Schrödinger, an heuristic point of view

Banff International Research Station for Mathematical Innovation and Discovery

We propose a generalization of the Schr\"odinger problem by replacing the usual entropy with a functional $\mathcal F$ which approaches the Wasserstein distance along the gradient of $\mathcal F$. From an heuristic point of view by using Otto calculus, we show that interpolations satisfy a Newton equation, extending the recent result of Giovani Conforti. Various inequalities as Evolutional-Variational-inequalities are also established from a heuristic point of view. As a rigorous result we prove a new and general contraction inequality for the usual Schr\"odinger problem under Ricci bound on a smooth and compact Riemannian manifold. This is a joint work with L. Ripani and C. L\'eonard.

Mathematics; Partial differential equations; Statistical mechanics, structure of matter

video/mp4

Author affiliation: Universite Lyon 1

2018-10-11

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/67468

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/