  We show that the configuration space over a manifold M inherits many
curvature properties of the manifold. For instance, we show that a lower Ricci
curvature bound on M implies for the configuration space a lower Ricci
curvature bound in the sense of Lott-Sturm-Villani, the Bochner inequality,
gradient estimates and Wasserstein contraction. Moreover, we show that the heat
flow on the configuration space, or the infinite independent particle process,
can be identified as the gradient flow of the entropy.
