The dynamical Schrodinger problem in abstract metric spaces

In this paper we introduce the dynamical Schrodinger prob-lem, defined for a wide class of entropy and Fisher informa-tion functionals, as a geometric problem on abstract metric spaces. Under very mild assumptions we prove a generic & UGamma;-convergence result towards the geodesic problem as the noise parameter & epsilon; & DARR;0. We also study the dependence of the entropic cost on the parameter & epsilon;. Some examples and applications are discussed.& COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).