{"_id":"17282","volume":63,"type":"journal_article","project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"status":"public","month":"07","oa_version":"Published Version","has_accepted_license":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).J. M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117), and by the Austrian Science Fund (FWF), Project SFB F65. We thank the anonymous referee for valuable comments on the paper.","scopus_import":"1","publication":"Calculus of Variations and Partial Differential Equations","date_updated":"2024-07-22T07:12:13Z","title":"Characterisation of gradient flows for a given functional","article_type":"original","author":[{"first_name":"Morris","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","last_name":"Brooks","orcid":"0000-0002-6249-0928","full_name":"Brooks, Morris"},{"last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338"}],"day":"01","issue":"6","date_published":"2024-07-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2024-07-22T07:05:32Z","quality_controlled":"1","doi":"10.1007/s00526-024-02755-z","intvolume":"        63","oa":1,"file":[{"access_level":"open_access","relation":"main_file","creator":"dernst","file_size":416622,"file_name":"2024_CalculusVariations_Brooks.pdf","date_updated":"2024-07-22T07:05:32Z","success":1,"file_id":"17289","date_created":"2024-07-22T07:05:32Z","checksum":"a0cf0e0ba2157aabb287cb597be17dac","content_type":"application/pdf"}],"abstract":[{"lang":"eng","text":"Let  X  be a vector field and  Y  be a co-vector field on a smooth manifold  M. Does there exist a smooth Riemannian metric  gαβ  on  M  such that  Yβ=gαβXα ? The main result of this note gives necessary and sufficient conditions for this to be true. As an application of this result we show that a finite-dimensional ergodic Lindblad equation admits a gradient flow structure for the von Neumann relative entropy if and only if the condition of BKM-detailed balance holds."}],"publication_identifier":{"issn":["0944-2669"],"eissn":["1432-0835"]},"ec_funded":1,"language":[{"iso":"eng"}],"corr_author":"1","external_id":{"arxiv":["2209.11149"]},"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)"},"publication_status":"published","citation":{"mla":"Brooks, Morris, and Jan Maas. “Characterisation of Gradient Flows for a given Functional.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 63, no. 6, 153, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00526-024-02755-z\">10.1007/s00526-024-02755-z</a>.","ista":"Brooks M, Maas J. 2024. Characterisation of gradient flows for a given functional. Calculus of Variations and Partial Differential Equations. 63(6), 153.","apa":"Brooks, M., &#38; Maas, J. (2024). Characterisation of gradient flows for a given functional. <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00526-024-02755-z\">https://doi.org/10.1007/s00526-024-02755-z</a>","chicago":"Brooks, Morris, and Jan Maas. “Characterisation of Gradient Flows for a given Functional.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00526-024-02755-z\">https://doi.org/10.1007/s00526-024-02755-z</a>.","ama":"Brooks M, Maas J. Characterisation of gradient flows for a given functional. <i>Calculus of Variations and Partial Differential Equations</i>. 2024;63(6). doi:<a href=\"https://doi.org/10.1007/s00526-024-02755-z\">10.1007/s00526-024-02755-z</a>","ieee":"M. Brooks and J. Maas, “Characterisation of gradient flows for a given functional,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 63, no. 6. Springer Nature, 2024.","short":"M. Brooks, J. Maas, Calculus of Variations and Partial Differential Equations 63 (2024)."},"article_number":"153","license":"https://creativecommons.org/licenses/by/4.0/","year":"2024","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"JaMa"}],"date_created":"2024-07-21T22:01:01Z","ddc":["510"],"publisher":"Springer Nature"}