Complete Gradient Estimates of Quantum Markov Semigroups

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...

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Detalles Bibliográficos
Autores principales: Wirth, Melchior, Zhang, Haonan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550562/
https://www.ncbi.nlm.nih.gov/pubmed/34776525
http://dx.doi.org/10.1007/s00220-021-04199-4
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author Wirth, Melchior
Zhang, Haonan
author_facet Wirth, Melchior
Zhang, Haonan
author_sort Wirth, Melchior
collection PubMed
description 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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spelling pubmed-85505622021-11-10 Complete Gradient Estimates of Quantum Markov Semigroups Wirth, Melchior Zhang, Haonan Commun Math Phys Article 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. Springer Berlin Heidelberg 2021-08-30 2021 /pmc/articles/PMC8550562/ /pubmed/34776525 http://dx.doi.org/10.1007/s00220-021-04199-4 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Wirth, Melchior
Zhang, Haonan
Complete Gradient Estimates of Quantum Markov Semigroups
title Complete Gradient Estimates of Quantum Markov Semigroups
title_full Complete Gradient Estimates of Quantum Markov Semigroups
title_fullStr Complete Gradient Estimates of Quantum Markov Semigroups
title_full_unstemmed Complete Gradient Estimates of Quantum Markov Semigroups
title_short Complete Gradient Estimates of Quantum Markov Semigroups
title_sort complete gradient estimates of quantum markov semigroups
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550562/
https://www.ncbi.nlm.nih.gov/pubmed/34776525
http://dx.doi.org/10.1007/s00220-021-04199-4
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