  We show that on a manifold whose Riemannian metric evolves under backwards
Ricci flow two Brownian motions can be coupled in such a way that the
expectation of their normalized L-distance is non-increasing. As an immediate
corollary we obtain a new proof of a recent result of Topping (J. reine angew.
Math. 636 (2009), 93-122), namely that the normalized L-transportation cost
between two solutions of the heat equation is non-increasing as well.
