We prove the correspondence between the solutions of the sub-elliptic heat equation in a Carnot group G and the gradient flows of the relative entropy functional in the Wasserstein space of probability measures on G. Our result completely answers a question left open in a previous paper by N. Juillet, where the same correspondence was proved for G = Hn, the n-dimensional Heisenberg group.
Heat and entropy flows in Carnot groups
Stefani G.
2020
Abstract
We prove the correspondence between the solutions of the sub-elliptic heat equation in a Carnot group G and the gradient flows of the relative entropy functional in the Wasserstein space of probability measures on G. Our result completely answers a question left open in a previous paper by N. Juillet, where the same correspondence was proved for G = Hn, the n-dimensional Heisenberg group.
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