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Entropic concavity and positive energy

Banff International Research Station for Mathematical Innovation and Discovery

On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by geodesic convexity properties of various entropies with respect to the Kantorovich-Rubinstein-Wasserstein square distance from optimal transportation. These notions also make sense in a (nonsmooth) metric measure setting, where they have found powerful applications. In this talk I describe the development of an analogous theory for lower Ricci curvature bounds in time-like directions on a Lorentzian manifold. In particular, by lifting fractional powers of the Lorentz distance (a.k.a. time separation function) to probability measures on spacetime, I show the strong energy condition of Penrose is equivalent to geodesic concavity of the Boltzmann-Shannon entropy there.

Mathematics; Partial differential equations; Statistical mechanics, structure of matter

video/mp4

Author affiliation: University of Toronto

2018-10-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/67418

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/