abstract: In this talk, we will describe how the theory of optimal transport can lead to new Ricci flow results independent of optimal transport itself. In particular, given a Ricci flow on a manifold M over a time interval I, we introduce a second time parameter, and define natural gradient Ricci solitons on the space-time MxI. As an application, we shall see how our construction encodes various of the monotonic quantities that underpin Perelman's work on Ricci flow, and how the different Harnack inequalities naturally arise as simple curvature conditions on the space-time solitons.