Complete gradient estimates of quantum Markov semigroups
arXiv:2007.13506 · doi:10.1007/s00220-021-04199-4
Abstract
In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors.
arXiv comment29 pages, some typos fixed, final version
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