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Displacement convexity of generalized relative entropies. II
We introduce a class of generalized relative entropies (inspired by the Bregman divergence in information theory) on the Wasserstein space over a weighted Riemannian or Finsler manifold.We prove that the convexity of all the entropies in this class is equivalent to the combination of the nonnegative weighted Ricci curvature and …