  When the Ricci curvature of a Riemannian manifold is not lower bounded by a
constant, but lower bounded by a continuous function, we give a new
characterization of this lower bound through the convexity of relative entropy
on the probability space over the Riemannian manifold. Hence, we generalize
K.T. Sturm and von Renesse's result (Comm. Pure Appl. Math. 2005) to the case
with non-constant lower bound of Ricci curvature.
