{"ec_funded":1,"corr_author":"1","issue":"2","title":"Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems","status":"public","department":[{"_id":"JaMa"}],"date_created":"2019-04-30T07:34:18Z","article_type":"original","article_processing_charge":"Yes (via OA deal)","page":"319-378","pmid":1,"isi":1,"publication_status":"published","doi":"10.1007/s10955-019-02434-w","_id":"6358","ddc":["500"],"language":[{"iso":"eng"}],"day":"01","oa_version":"Published Version","oa":1,"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."}],"publication":"Journal of Statistical Physics","related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1007/s10955-020-02671-4"}]},"has_accepted_license":"1","publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"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","name":"Taming Complexity in Partial Differential Systems","grant_number":"F06504"}],"author":[{"first_name":"Eric A.","full_name":"Carlen, Eric A.","last_name":"Carlen"},{"full_name":"Maas, Jan","last_name":"Maas","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"}],"file_date_updated":"2020-07-14T12:47:28Z","volume":178,"intvolume":"       178","date_published":"2020-01-01T00:00:00Z","file":[{"access_level":"open_access","date_created":"2019-12-23T12:03:09Z","file_id":"7209","file_name":"2019_JourStatistPhysics_Carlen.pdf","file_size":905538,"relation":"main_file","checksum":"7b04befbdc0d4982c0ee945d25d19872","creator":"dernst","content_type":"application/pdf","date_updated":"2020-07-14T12:47:28Z"}],"quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"01","scopus_import":"1","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"},"external_id":{"arxiv":["1811.04572"],"isi":["000498933300001"],"pmid":["33223567"]},"date_updated":"2025-06-12T07:27:20Z","citation":{"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.","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>.","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>","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>."},"type":"journal_article","year":"2020","publisher":"Springer Nature","arxiv":1}