{"oa":1,"title":"Complete gradient estimates of quantum Markov semigroups","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["621"],"intvolume":"       387","date_published":"2021-08-30T00:00:00Z","external_id":{"isi":["000691214200001"],"arxiv":["2007.13506"]},"ec_funded":1,"doi":"10.1007/s00220-021-04199-4","article_processing_charge":"Yes (via OA deal)","citation":{"apa":"Wirth, M., &#38; Zhang, H. (2021). Complete gradient estimates of quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-021-04199-4\">https://doi.org/10.1007/s00220-021-04199-4</a>","short":"M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.","ista":"Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 387, 761–791.","mla":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>, vol. 387, Springer Nature, 2021, pp. 761–791, doi:<a href=\"https://doi.org/10.1007/s00220-021-04199-4\">10.1007/s00220-021-04199-4</a>.","ieee":"M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,” <i>Communications in Mathematical Physics</i>, vol. 387. Springer Nature, pp. 761–791, 2021.","ama":"Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. 2021;387:761–791. doi:<a href=\"https://doi.org/10.1007/s00220-021-04199-4\">10.1007/s00220-021-04199-4</a>","chicago":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-021-04199-4\">https://doi.org/10.1007/s00220-021-04199-4</a>."},"article_type":"original","quality_controlled":"1","has_accepted_license":"1","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"abstract":[{"lang":"eng","text":"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."}],"isi":1,"publisher":"Springer Nature","type":"journal_article","file_date_updated":"2021-09-08T09:46:34Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"30","year":"2021","volume":387,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"language":[{"iso":"eng"}],"date_updated":"2023-08-11T11:09:07Z","date_created":"2021-08-30T10:07:44Z","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"publication_status":"published","month":"08","file":[{"relation":"main_file","file_name":"2021_CommunMathPhys_Wirth.pdf","file_size":505971,"creator":"cchlebak","access_level":"open_access","date_created":"2021-09-08T07:34:24Z","date_updated":"2021-09-08T09:46:34Z","file_id":"9990","content_type":"application/pdf","checksum":"8a602f916b1c2b0dc1159708b7cb204b"}],"scopus_import":"1","oa_version":"Published Version","_id":"9973","status":"public","author":[{"orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","full_name":"Wirth, Melchior","first_name":"Melchior"},{"last_name":"Zhang","full_name":"Zhang, Haonan","first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425"}],"publication":"Communications in Mathematical Physics","department":[{"_id":"JaMa"}],"page":"761–791","acknowledgement":"Both authors would like to thank Jan Maas for fruitful discussions and helpful comments."}