1986/01/01 by Melchior Wirth, Haonan Zhang, Juan Antonio Tomás Carpi · 1 voice · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · Social Sciences · #Advanced Operator Algebra Research #Art #Constant (computer programming) #Free probability #Geography #Geometric Analysis and Curvature Flows #Historical and socio-economic studies of Spain and related regions #Humanities #Logarithm #Markov Chains and Monte Carlo Methods #Markov chain #Noncommutative geometry #Quantum #Regional Development and Innovation #Semigroup #Urbanism, Landscape, and Tourism Studies #Von Neumann entropy #math-ph #math.FA #math.MP #math.OA
paper · pdf · doi:10.1007/s00220-021-04199-4
published as Commun. Math. Phys. (2021) · 29 pages, some typos fixed, final version
openalex publication_date 1986/01/01 · openalex created_date 2016/06/24 · arxiv published 2020/07/27 · arxiv created 2021/09/03 · arxiv updated 2021/09/06 · openalex updated_date 2026/04/28
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.