[{"date_published":"2023-08-15T00:00:00Z","type":"journal_article","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2106.11217","open_access":"1"}],"status":"public","related_material":{"record":[{"id":"9792","relation":"earlier_version","status":"public"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Journal of Functional Analysis","oa_version":"Preprint","project":[{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"},{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"260482E2-B435-11E9-9278-68D0E5697425","name":"Taming Complexity in Partial Di erential Systems","grant_number":" F06504"}],"month":"08","article_number":"109963","language":[{"iso":"eng"}],"date_updated":"2023-11-14T13:21:01Z","citation":{"ista":"Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 285(4), 109963.","short":"D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023).","mla":"Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>Journal of Functional Analysis</i>, vol. 285, no. 4, 109963, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">10.1016/j.jfa.2023.109963</a>.","chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>Journal of Functional Analysis</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">https://doi.org/10.1016/j.jfa.2023.109963</a>.","ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” <i>Journal of Functional Analysis</i>, vol. 285, no. 4. Elsevier, 2023.","ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>Journal of Functional Analysis</i>. 2023;285(4). doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">10.1016/j.jfa.2023.109963</a>","apa":"Feliciangeli, D., Gerolin, A., &#38; Portinale, L. (2023). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">https://doi.org/10.1016/j.jfa.2023.109963</a>"},"year":"2023","isi":1,"external_id":{"arxiv":["2106.11217"],"isi":["000990804300001"]},"doi":"10.1016/j.jfa.2023.109963","arxiv":1,"day":"15","abstract":[{"lang":"eng","text":"This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem."}],"acknowledgement":"This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. The authors also thank J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. Finally, we acknowledge the high quality review done by the anonymous referee of our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813.","volume":285,"_id":"12911","scopus_import":"1","author":[{"last_name":"Feliciangeli","first_name":"Dario","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","id":"41A639AA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Augusto","last_name":"Gerolin","full_name":"Gerolin, Augusto"},{"first_name":"Lorenzo","last_name":"Portinale","full_name":"Portinale, Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"}],"issue":"4","publication_status":"published","department":[{"_id":"RoSe"},{"_id":"JaMa"}],"date_created":"2023-05-07T22:01:02Z","article_processing_charge":"No","title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","intvolume":"       285","ec_funded":1,"quality_controlled":"1","publisher":"Elsevier","article_type":"original"},{"day":"01","doi":"10.1007/s10955-020-02663-4","arxiv":1,"abstract":[{"text":"We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary Γ-convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.","lang":"eng"}],"citation":{"ieee":"J. Maas and A. Mielke, “Modeling of chemical reaction systems with detailed balance using gradient structures,” <i>Journal of Statistical Physics</i>, vol. 181, no. 6. Springer Nature, pp. 2257–2303, 2020.","chicago":"Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures.” <i>Journal of Statistical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s10955-020-02663-4\">https://doi.org/10.1007/s10955-020-02663-4</a>.","apa":"Maas, J., &#38; Mielke, A. (2020). Modeling of chemical reaction systems with detailed balance using gradient structures. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-020-02663-4\">https://doi.org/10.1007/s10955-020-02663-4</a>","ama":"Maas J, Mielke A. Modeling of chemical reaction systems with detailed balance using gradient structures. <i>Journal of Statistical Physics</i>. 2020;181(6):2257-2303. doi:<a href=\"https://doi.org/10.1007/s10955-020-02663-4\">10.1007/s10955-020-02663-4</a>","ista":"Maas J, Mielke A. 2020. Modeling of chemical reaction systems with detailed balance using gradient structures. Journal of Statistical Physics. 181(6), 2257–2303.","mla":"Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures.” <i>Journal of Statistical Physics</i>, vol. 181, no. 6, Springer Nature, 2020, pp. 2257–303, doi:<a href=\"https://doi.org/10.1007/s10955-020-02663-4\">10.1007/s10955-020-02663-4</a>.","short":"J. Maas, A. Mielke, Journal of Statistical Physics 181 (2020) 2257–2303."},"year":"2020","date_updated":"2023-08-22T13:24:27Z","external_id":{"arxiv":["2004.02831"],"isi":["000587107200002"]},"isi":1,"acknowledgement":"The research of A.M. was partially supported by the Deutsche Forschungsgemeinschaft (DFG) via the Collaborative Research Center SFB 1114 Scaling Cascades in Complex Systems (Project No. 235221301), through the Subproject C05 Effective models for materials and interfaces with multiple scales. 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. The authors thank Christof Schütte, Robert I. A. Patterson, and Stefanie Winkelmann for helpful and stimulating discussions. Open access funding provided by Austrian Science Fund (FWF).","volume":181,"ddc":["510"],"article_processing_charge":"No","date_created":"2020-11-15T23:01:18Z","department":[{"_id":"JaMa"}],"publication_status":"published","intvolume":"       181","title":"Modeling of chemical reaction systems with detailed balance using gradient structures","scopus_import":"1","_id":"8758","issue":"6","author":[{"orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","first_name":"Jan","last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mielke, Alexander","first_name":"Alexander","last_name":"Mielke"}],"publisher":"Springer Nature","article_type":"original","ec_funded":1,"quality_controlled":"1","page":"2257-2303","file_date_updated":"2021-02-04T10:29:11Z","publication_identifier":{"issn":["00224715"],"eissn":["15729613"]},"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2020-12-01T00:00:00Z","file":[{"date_updated":"2021-02-04T10:29:11Z","file_name":"2020_JourStatPhysics_Maas.pdf","content_type":"application/pdf","date_created":"2021-02-04T10:29:11Z","checksum":"bc2b63a90197b97cbc73eccada4639f5","file_size":753596,"file_id":"9087","creator":"dernst","success":1,"relation":"main_file","access_level":"open_access"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Taming Complexity in Partial Di erential Systems","grant_number":" F06504","_id":"260482E2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"oa_version":"Published Version","month":"12","has_accepted_license":"1","publication":"Journal of Statistical Physics","language":[{"iso":"eng"}]},{"date_published":"2020-07-01T00:00:00Z","type":"journal_article","oa":1,"publication_identifier":{"issn":["00217824"]},"status":"public","related_material":{"record":[{"relation":"dissertation_contains","id":"10030","status":"public"}]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1905.05757"}],"publication":"Journal de Mathematiques Pures et Appliquees","month":"07","oa_version":"Preprint","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":" F06504","name":"Taming Complexity in Partial Di erential Systems","_id":"260482E2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"isi":1,"external_id":{"arxiv":["1905.05757"],"isi":["000539439400008"]},"date_updated":"2023-09-07T13:31:05Z","year":"2020","citation":{"short":"P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Journal de Mathematiques Pures et Appliquees 139 (2020) 204–234.","mla":"Gladbach, Peter, et al. “Homogenisation of One-Dimensional Discrete Optimal Transport.” <i>Journal de Mathematiques Pures et Appliquees</i>, vol. 139, no. 7, Elsevier, 2020, pp. 204–34, doi:<a href=\"https://doi.org/10.1016/j.matpur.2020.02.008\">10.1016/j.matpur.2020.02.008</a>.","ista":"Gladbach P, Kopfer E, Maas J, Portinale L. 2020. Homogenisation of one-dimensional discrete optimal transport. Journal de Mathematiques Pures et Appliquees. 139(7), 204–234.","apa":"Gladbach, P., Kopfer, E., Maas, J., &#38; Portinale, L. (2020). Homogenisation of one-dimensional discrete optimal transport. <i>Journal de Mathematiques Pures et Appliquees</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.matpur.2020.02.008\">https://doi.org/10.1016/j.matpur.2020.02.008</a>","ama":"Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of one-dimensional discrete optimal transport. <i>Journal de Mathematiques Pures et Appliquees</i>. 2020;139(7):204-234. doi:<a href=\"https://doi.org/10.1016/j.matpur.2020.02.008\">10.1016/j.matpur.2020.02.008</a>","chicago":"Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of One-Dimensional Discrete Optimal Transport.” <i>Journal de Mathematiques Pures et Appliquees</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.matpur.2020.02.008\">https://doi.org/10.1016/j.matpur.2020.02.008</a>.","ieee":"P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of one-dimensional discrete optimal transport,” <i>Journal de Mathematiques Pures et Appliquees</i>, vol. 139, no. 7. Elsevier, pp. 204–234, 2020."},"abstract":[{"lang":"eng","text":"This paper deals with dynamical optimal transport metrics defined by spatial discretisation of the Benamou–Benamou formula for the Kantorovich metric . Such metrics appear naturally in discretisations of -gradient flow formulations for dissipative PDE. However, it has recently been shown that these metrics do not in general converge to , unless strong geometric constraints are imposed on the discrete mesh. In this paper we prove that, in a 1-dimensional periodic setting, discrete transport metrics converge to a limiting transport metric with a non-trivial effective mobility. This mobility depends sensitively on the geometry of the mesh and on the non-local mobility at the discrete level. Our result quantifies to what extent discrete transport can make use of microstructure in the mesh to reduce the cost of transport."}],"doi":"10.1016/j.matpur.2020.02.008","arxiv":1,"day":"01","volume":139,"acknowledgement":"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). J.M. and L.P. also acknowledge support from the Austrian Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support by the German Research Foundation through the Hausdorff Center for Mathematics and the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 350398276.","author":[{"full_name":"Gladbach, Peter","first_name":"Peter","last_name":"Gladbach"},{"last_name":"Kopfer","first_name":"Eva","full_name":"Kopfer, Eva"},{"full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","full_name":"Portinale, Lorenzo","first_name":"Lorenzo","last_name":"Portinale"}],"issue":"7","_id":"7573","scopus_import":"1","title":"Homogenisation of one-dimensional discrete optimal transport","intvolume":"       139","publication_status":"published","article_processing_charge":"No","date_created":"2020-03-08T23:00:47Z","department":[{"_id":"JaMa"}],"page":"204-234","ec_funded":1,"quality_controlled":"1","article_type":"original","publisher":"Elsevier"},{"issue":"2","author":[{"first_name":"Eric A.","last_name":"Carlen","full_name":"Carlen, Eric A."},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas","first_name":"Jan"}],"scopus_import":"1","_id":"6358","intvolume":"       178","title":"Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems","department":[{"_id":"JaMa"}],"date_created":"2019-04-30T07:34:18Z","article_processing_charge":"Yes (via OA deal)","publication_status":"published","file_date_updated":"2020-07-14T12:47:28Z","quality_controlled":"1","ec_funded":1,"page":"319-378","article_type":"original","publisher":"Springer Nature","external_id":{"isi":["000498933300001"],"arxiv":["1811.04572"]},"isi":1,"citation":{"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>.","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>","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>","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.","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.” <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>."},"year":"2020","date_updated":"2023-08-17T13:49:40Z","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"}],"day":"01","doi":"10.1007/s10955-019-02434-w","arxiv":1,"ddc":["500"],"volume":178,"has_accepted_license":"1","publication":"Journal of Statistical Physics","month":"01","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"},{"grant_number":" F06504","name":"Taming Complexity in Partial Di erential Systems","_id":"260482E2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"oa_version":"Published Version","language":[{"iso":"eng"}],"type":"journal_article","date_published":"2020-01-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"eissn":["15729613"],"issn":["00224715"]},"status":"public","related_material":{"link":[{"url":"https://doi.org/10.1007/s10955-020-02671-4","relation":"erratum"}]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"file_size":905538,"checksum":"7b04befbdc0d4982c0ee945d25d19872","date_created":"2019-12-23T12:03:09Z","content_type":"application/pdf","file_name":"2019_JourStatistPhysics_Carlen.pdf","date_updated":"2020-07-14T12:47:28Z","relation":"main_file","access_level":"open_access","creator":"dernst","file_id":"7209"}]},{"ec_funded":1,"quality_controlled":"1","file_date_updated":"2020-07-14T12:47:55Z","publisher":"Springer","article_type":"original","_id":"73","scopus_import":"1","author":[{"full_name":"Erbar, Matthias","last_name":"Erbar","first_name":"Matthias"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas","first_name":"Jan"},{"first_name":"Melchior","last_name":"Wirth","full_name":"Wirth, Melchior"}],"issue":"1","publication_status":"published","date_created":"2018-12-11T11:44:29Z","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"JaMa"}],"title":"On the geometry of geodesics in discrete optimal transport","intvolume":"        58","volume":58,"ddc":["510"],"date_updated":"2023-09-13T09:12:35Z","year":"2019","citation":{"apa":"Erbar, M., Maas, J., &#38; Wirth, M. (2019). On the geometry of geodesics in discrete optimal transport. <i>Calculus of Variations and Partial Differential Equations</i>. Springer. <a href=\"https://doi.org/10.1007/s00526-018-1456-1\">https://doi.org/10.1007/s00526-018-1456-1</a>","ama":"Erbar M, Maas J, Wirth M. On the geometry of geodesics in discrete optimal transport. <i>Calculus of Variations and Partial Differential Equations</i>. 2019;58(1). doi:<a href=\"https://doi.org/10.1007/s00526-018-1456-1\">10.1007/s00526-018-1456-1</a>","chicago":"Erbar, Matthias, Jan Maas, and Melchior Wirth. “On the Geometry of Geodesics in Discrete Optimal Transport.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s00526-018-1456-1\">https://doi.org/10.1007/s00526-018-1456-1</a>.","ieee":"M. Erbar, J. Maas, and M. Wirth, “On the geometry of geodesics in discrete optimal transport,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 58, no. 1. Springer, 2019.","mla":"Erbar, Matthias, et al. “On the Geometry of Geodesics in Discrete Optimal Transport.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 58, no. 1, 19, Springer, 2019, doi:<a href=\"https://doi.org/10.1007/s00526-018-1456-1\">10.1007/s00526-018-1456-1</a>.","short":"M. Erbar, J. Maas, M. Wirth, Calculus of Variations and Partial Differential Equations 58 (2019).","ista":"Erbar M, Maas J, Wirth M. 2019. On the geometry of geodesics in discrete optimal transport. Calculus of Variations and Partial Differential Equations. 58(1), 19."},"isi":1,"external_id":{"isi":["000452849400001"],"arxiv":["1805.06040"]},"doi":"10.1007/s00526-018-1456-1","arxiv":1,"day":"01","abstract":[{"text":"We consider the space of probability measures on a discrete set X, endowed with a dynamical optimal transport metric. Given two probability measures supported in a subset Y⊆X, it is natural to ask whether they can be connected by a constant speed geodesic with support in Y at all times. Our main result answers this question affirmatively, under a suitable geometric condition on Y introduced in this paper. The proof relies on an extension result for subsolutions to discrete Hamilton-Jacobi equations, which is of independent interest.","lang":"eng"}],"language":[{"iso":"eng"}],"publication":"Calculus of Variations and Partial Differential Equations","has_accepted_license":"1","oa_version":"Published Version","project":[{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":" F06504","name":"Taming Complexity in Partial Di erential Systems","call_identifier":"FWF","_id":"260482E2-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"month":"02","article_number":"19","file":[{"relation":"main_file","access_level":"open_access","file_id":"5895","creator":"dernst","date_created":"2019-01-28T15:37:11Z","checksum":"ba05ac2d69de4c58d2cd338b63512798","file_size":645565,"date_updated":"2020-07-14T12:47:55Z","file_name":"2018_Calculus_Erbar.pdf","content_type":"application/pdf"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2019-02-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["09442669"]},"oa":1}]