{"publisher":"Springer Nature","date_created":"2019-04-30T07:34:18Z","issue":"2","title":"Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems","arxiv":1,"article_type":"original","article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Carlen","full_name":"Carlen, Eric A.","first_name":"Eric A."},{"full_name":"Maas, Jan","first_name":"Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas"}],"year":"2020","doi":"10.1007/s10955-019-02434-w","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"status":"public","oa":1,"oa_version":"Published Version","day":"01","publication_status":"published","has_accepted_license":"1","date_updated":"2025-06-12T07:27:20Z","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"corr_author":"1","external_id":{"pmid":["33223567"],"isi":["000498933300001"],"arxiv":["1811.04572"]},"file_date_updated":"2020-07-14T12:47:28Z","month":"01","scopus_import":"1","department":[{"_id":"JaMa"}],"abstract":[{"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.","lang":"eng"}],"_id":"6358","page":"319-378","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"},{"_id":"260482E2-B435-11E9-9278-68D0E5697425","grant_number":"F06504","name":"Taming Complexity in Partial Differential Systems","call_identifier":"FWF"}],"isi":1,"citation":{"mla":"Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities  in Dissipative Quantum Systems.” <i>Journal of Statistical Physics</i>, vol. 178, no. 2, Springer Nature, 2020, pp. 319–78, doi:<a href=\"https://doi.org/10.1007/s10955-019-02434-w\">10.1007/s10955-019-02434-w</a>.","short":"E.A. Carlen, J. Maas, Journal of Statistical Physics 178 (2020) 319–378.","apa":"Carlen, E. A., &#38; Maas, J. (2020). Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-019-02434-w\">https://doi.org/10.1007/s10955-019-02434-w</a>","ieee":"E. A. Carlen and J. Maas, “Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems,” <i>Journal of Statistical Physics</i>, vol. 178, no. 2. Springer Nature, pp. 319–378, 2020.","ama":"Carlen EA, Maas J. Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. <i>Journal of Statistical Physics</i>. 2020;178(2):319-378. doi:<a href=\"https://doi.org/10.1007/s10955-019-02434-w\">10.1007/s10955-019-02434-w</a>","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.” <i>Journal of Statistical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s10955-019-02434-w\">https://doi.org/10.1007/s10955-019-02434-w</a>."},"ddc":["500"],"type":"journal_article","ec_funded":1,"file":[{"file_id":"7209","file_name":"2019_JourStatistPhysics_Carlen.pdf","file_size":905538,"date_updated":"2020-07-14T12:47:28Z","access_level":"open_access","creator":"dernst","relation":"main_file","content_type":"application/pdf","checksum":"7b04befbdc0d4982c0ee945d25d19872","date_created":"2019-12-23T12:03:09Z"}],"intvolume":"       178","pmid":1,"related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1007/s10955-020-02671-4"}]},"quality_controlled":"1","publication":"Journal of Statistical Physics","date_published":"2020-01-01T00:00:00Z","volume":178}