01451nas a2200133   4500008004100000022001400041245008500055210007100140260000800211520101400219100001801233700001901251856004701270       2019                        eng d  a1432-206400aBenamou–Brenier and duality formulas for the entropic cost on RCD*(K,N) spaces0 aBenamou–Brenier and duality formulas for the entropic cost on RC  cApr3 a<p>In this paper we prove that, within the framework of $\textsf{RCD}^\star(K,N)$ spaces with $N&lt;\infty$, the entropic cost (i.e. the minimal value of the Schrödinger problem) admits:A threefold dynamical variational representation, in the spirit of the Benamou–Brenier formula for the Wasserstein distance; A Hamilton–Jacobi–Bellman dual representation, in line with Bobkov–Gentil–Ledoux and Otto–Villani results on the duality between Hamilton–Jacobi and continuity equation for optimal transport;A Kantorovich-type duality formula, where the Hopf–Lax semigroup is replaced by a suitable `entropic' counterpart.We thus provide a complete and unifying picture of the equivalent variational representations of the Schrödinger problem as well as a perfect parallelism with the analogous formulas for the Wasserstein distance. Riemannian manifolds with Ricci curvature bounded from below are a relevant class of $\textsf{RCD}^*(K,N)$ spaces and our results are new even in this setting.</p>1 aGigli, Nicola1 aTamanini, Luca  uhttps://doi.org/10.1007/s00440-019-00909-1