[{"scopus_import":"1","month":"01","intvolume":" 178","abstract":[{"lang":"eng","text":"We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral gap estimates."}],"oa_version":"Published Version","related_material":{"link":[{"url":"https://doi.org/10.1007/s10955-020-02671-4","relation":"erratum"}]},"volume":178,"issue":"2","ec_funded":1,"publication_identifier":{"eissn":["15729613"],"issn":["00224715"]},"publication_status":"published","file":[{"date_updated":"2020-07-14T12:47:28Z","file_size":905538,"creator":"dernst","date_created":"2019-12-23T12:03:09Z","file_name":"2019_JourStatistPhysics_Carlen.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"7b04befbdc0d4982c0ee945d25d19872","file_id":"7209"}],"language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"6358","department":[{"_id":"JaMa"}],"file_date_updated":"2020-07-14T12:47:28Z","date_updated":"2023-08-17T13:49:40Z","ddc":["500"],"publisher":"Springer Nature","quality_controlled":"1","oa":1,"page":"319-378","date_published":"2020-01-01T00:00:00Z","doi":"10.1007/s10955-019-02434-w","date_created":"2019-04-30T07:34:18Z","isi":1,"has_accepted_license":"1","year":"2020","day":"01","publication":"Journal of Statistical Physics","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"call_identifier":"FWF","_id":"260482E2-B435-11E9-9278-68D0E5697425","grant_number":" F06504","name":"Taming Complexity in Partial Di erential Systems"}],"author":[{"first_name":"Eric A.","last_name":"Carlen","full_name":"Carlen, Eric A."},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Maas","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000498933300001"],"arxiv":["1811.04572"]},"title":"Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems","citation":{"ista":"Carlen EA, Maas J. 2020. Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems. Journal of Statistical Physics. 178(2), 319–378.","chicago":"Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems.” Journal of Statistical Physics. Springer Nature, 2020. https://doi.org/10.1007/s10955-019-02434-w.","apa":"Carlen, E. A., & Maas, J. (2020). Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-019-02434-w","ama":"Carlen EA, Maas J. Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems. Journal of Statistical Physics. 2020;178(2):319-378. doi:10.1007/s10955-019-02434-w","ieee":"E. A. Carlen and J. Maas, “Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems,” Journal of Statistical Physics, vol. 178, no. 2. Springer Nature, pp. 319–378, 2020.","short":"E.A. Carlen, J. Maas, Journal of Statistical Physics 178 (2020) 319–378.","mla":"Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems.” Journal of Statistical Physics, vol. 178, no. 2, Springer Nature, 2020, pp. 319–78, doi:10.1007/s10955-019-02434-w."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"}]