Complete gradient estimates of quantum Markov semigroups - Wirth, Melchior; Zhang, Haonan; IST Austria Open Access Fund; ISTplus - Postdoctoral Fellowships; Taming Complexity in Partial Differential Systems (Communications in Mathematical Physics, 2021)
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.
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Keywords: article; Mathematical Physics -- Statistical and Nonlinear Physics