{"isi":1,"acknowledgement":"The author wants to thank Jan Maas for helpful comments. He also acknowledges financial support from the Austrian Science Fund (FWF) through Grant Number F65 and from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (Grant Agreement No. 716117).\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","ddc":["510","530"],"abstract":[{"lang":"eng","text":"In this article we study the noncommutative transport distance introduced by Carlen and Maas and its entropic regularization defined by Becker and Li. We prove a duality formula that can be understood as a quantum version of the dual Benamou–Brenier formulation of the Wasserstein distance in terms of subsolutions of a Hamilton–Jacobi–Bellmann equation."}],"doi":"10.1007/s10955-022-02911-9","month":"04","publication_identifier":{"eissn":["15729613"],"issn":["00224715"]},"publication":"Journal of Statistical Physics","volume":187,"status":"public","oa_version":"Published Version","_id":"11330","has_accepted_license":"1","citation":{"mla":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” <i>Journal of Statistical Physics</i>, vol. 187, no. 2, 19, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s10955-022-02911-9\">10.1007/s10955-022-02911-9</a>.","apa":"Wirth, M. (2022). A dual formula for the noncommutative transport distance. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-022-02911-9\">https://doi.org/10.1007/s10955-022-02911-9</a>","ieee":"M. Wirth, “A dual formula for the noncommutative transport distance,” <i>Journal of Statistical Physics</i>, vol. 187, no. 2. Springer Nature, 2022.","ama":"Wirth M. A dual formula for the noncommutative transport distance. <i>Journal of Statistical Physics</i>. 2022;187(2). doi:<a href=\"https://doi.org/10.1007/s10955-022-02911-9\">10.1007/s10955-022-02911-9</a>","short":"M. Wirth, Journal of Statistical Physics 187 (2022).","ista":"Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 187(2), 19.","chicago":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” <i>Journal of Statistical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10955-022-02911-9\">https://doi.org/10.1007/s10955-022-02911-9</a>."},"issue":"2","file":[{"file_name":"2022_JourStatisticalPhysics_Wirth.pdf","content_type":"application/pdf","date_updated":"2022-04-29T11:24:23Z","creator":"dernst","checksum":"f3e0b00884b7dde31347a3756788b473","file_id":"11338","success":1,"date_created":"2022-04-29T11:24:23Z","file_size":362119,"relation":"main_file","access_level":"open_access"}],"date_created":"2022-04-24T22:01:43Z","author":[{"orcid":"0000-0002-0519-4241","last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior","first_name":"Melchior"}],"scopus_import":"1","intvolume":"       187","day":"08","title":"A dual formula for the noncommutative transport distance","date_updated":"2023-08-03T06:37:49Z","department":[{"_id":"JaMa"}],"publication_status":"published","publisher":"Springer Nature","type":"journal_article","ec_funded":1,"article_processing_charge":"Yes (via OA deal)","article_number":"19","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"year":"2022","external_id":{"isi":["000780305000001"]},"date_published":"2022-04-08T00:00:00Z","file_date_updated":"2022-04-29T11:24:23Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_type":"original","oa":1,"quality_controlled":"1","language":[{"iso":"eng"}],"project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}]}