{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:48:18Z","timestamp":1774626498179,"version":"3.50.1"},"publisher-location":"Cham","reference-count":18,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030802080","type":"print"},{"value":"9783030802097","type":"electronic"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-80209-7_27","type":"book-chapter","created":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T00:02:40Z","timestamp":1626220960000},"page":"237-244","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Gibbs States on Symplectic Manifolds with Symmetries"],"prefix":"10.1007","author":[{"given":"Charles-Michel","family":"Marle","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,14]]},"reference":[{"key":"27_CR1","doi-asserted-by":"publisher","first-page":"4521","DOI":"10.3390\/e16084521","volume":"16","author":"F Barbaresco","year":"2014","unstructured":"Barbaresco, F.: Koszul information geometry and Souriau geometric temperature\/capacity of Lie group thermodynamics. Entropy 16, 4521\u20134565 (2014)","journal-title":"Entropy"},{"key":"27_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1007\/978-3-319-25040-3_57","volume-title":"Geometric Science of Information","author":"F Barbaresco","year":"2015","unstructured":"Barbaresco, F.: Symplectic structure of information geometry: fisher metric and Euler-Poincar\u00e9 equation of Souriau Lie group thermodynamics. In: Nielsen, F., Barbaresco, F. (eds.) GSI 2015. LNCS, vol. 9389, pp. 529\u2013540. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-25040-3_57"},{"key":"27_CR3","doi-asserted-by":"publisher","unstructured":"Barbaresco, F.: Geometric Theory of Heat from Souriau Lie Groups thermodynamics and Koszul Hessian geometry: applications in information geometry for exponential families. Entropy 18(11), 386 (2016). https:\/\/doi.org\/10.3390\/e18110386. In the Special Issue \u201cDifferential Geometrical Theory of Statistics\u201d, MDPI","DOI":"10.3390\/e18110386"},{"key":"27_CR4","doi-asserted-by":"publisher","first-page":"642","DOI":"10.3390\/e22060642","volume":"22","author":"F Barbaresco","year":"2020","unstructured":"Barbaresco, F.: Lie group statistics and Lie group machine learning based on Souriau lie groups thermodynamics and Koszul-Souriau-fisher metric: new entropy definition as Casimir invariant function in coadjoint representation. Entropy 22, 642 (2020). https:\/\/doi.org\/10.3390\/e22060642","journal-title":"Entropy"},{"key":"27_CR5","doi-asserted-by":"publisher","first-page":"498","DOI":"10.3390\/e22050498","volume":"22","author":"F Barbaresco","year":"2020","unstructured":"Barbaresco, F., Gay-Balmaz, F.: Lie group cohomology and (multi)symplectic integrators: new geometric tools for Lie group machine learning based on Souriau geometric statistical mechanics. Entropy 22, 498 (2020). https:\/\/doi.org\/10.3390\/e22050498","journal-title":"Entropy"},{"key":"27_CR6","doi-asserted-by":"crossref","unstructured":"Gibbs, W.: Elementary Principles in Statistical Mechanics, Developed with Especial Reference to the Rational Foundation of Thermodynamics. Charles Scribner\u2019s Sons, New York, Edward Arnold, London (1902). This public-domain ebook may be downloaded gratis at www.gutenberg.org\/ebooks\/50992","DOI":"10.5962\/bhl.title.32624"},{"key":"27_CR7","doi-asserted-by":"publisher","unstructured":"Marle, C.-M.: From tools in symplectic and Poisson geometry to J.-M. Souriau\u2019s theories of statistical mechanics and thermodynamics. Entropy 18, 370 (2016). https:\/\/doi.org\/10.3390\/e18100370","DOI":"10.3390\/e18100370"},{"key":"27_CR8","volume-title":"G\u00e9om\u00e9trie Symplectique et G\u00e9om\u00e9trie de Poisson","author":"C-M Marle","year":"2018","unstructured":"Marle, C.-M.: G\u00e9om\u00e9trie Symplectique et G\u00e9om\u00e9trie de Poisson. Calvage & Mounet, Paris (2018)"},{"key":"27_CR9","doi-asserted-by":"publisher","first-page":"45","DOI":"10.7546\/jgsp-57-2020-45-85","volume":"57","author":"C-M Marle","year":"2020","unstructured":"Marle, C.-M.: On Gibbs states of mechanical systems with symmetries. J. Geom. Symm. Phys. 57, 45\u201385 (2020). https:\/\/doi.org\/10.7546\/jgsp-57-2020-45-85","journal-title":"J. Geom. Symm. Phys."},{"key":"27_CR10","doi-asserted-by":"publisher","first-page":"55","DOI":"10.7546\/jgsp-58-2020-55-79","volume":"58","author":"C-M Marle","year":"2020","unstructured":"Marle, C.-M.: Examples of Gibbs states of mechanical systems with symmetries. J. Geom. Symm. Phys. 58, 55\u201379 (2020). https:\/\/doi.org\/10.7546\/jgsp-58-2020-55-79","journal-title":"J. Geom. Symm. Phys."},{"key":"27_CR11","unstructured":"Marle, C.-M.: On Gibbs states of mechanical systems with symmetries, 13 January 2021. arXiv:2012.00582v2"},{"key":"27_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1007\/978-3-319-25040-3_56","volume-title":"Geometric Science of Information","author":"G Saxc\u00e9","year":"2015","unstructured":"Saxc\u00e9, G.: Entropy and structure of the thermodynamical systems. In: Nielsen, F., Barbaresco, F. (eds.) GSI 2015. LNCS, vol. 9389, pp. 519\u2013528. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-25040-3_56"},{"key":"27_CR13","doi-asserted-by":"publisher","unstructured":"de Saxc\u00e9, G.: Link between Lie group statistical mechanics and thermodynamics of continua. Entropy 18, 254 (2016). https:\/\/doi.org\/10.3390\/e18070254. In the special Issue \u201cDifferential Geometrical Theory of Statistics, MDPI","DOI":"10.3390\/e18070254"},{"key":"27_CR14","unstructured":"Souriau, J.-M.: D\u00e9finition Covariante des \u00c9quilibres Thermodynamiques, Supplemento al Nuovo cimento, vol. IV n.1, pp. 203\u2013216 (1966)"},{"key":"27_CR15","unstructured":"Souriau, J.-M.: Structure des Syst\u00e8mes Dynamiques, Dunod, Paris, 1969. English translation: Structure of Dynamical Systems, a Symplectic View of Physics, translated by C. H. Cushman-de Vries, (Transl. Cushman, R.H., Tuynman) G.M. Progress in Mathematics volume 149, Birkh\u00e4user Boston (1997)"},{"key":"27_CR16","unstructured":"Souriau, J.-M.: M\u00e9canique Statistique, Groupes de Lie et Cosmologie, Colloques internationaux du CNRS num\u00e9ro 237 G\u00e9om\u00e9trie Symplectique et Physique Math\u00e9matique, pp. 59\u2013113 (1974)"},{"key":"27_CR17","unstructured":"Souriau, J.-M.: G\u00e9om\u00e9trie Symplectique et Physique Math\u00e9matique, deux conf\u00e9rences de Jean-Marie Souriau, Colloquium de la Soci\u00e9t\u00e9 Math\u00e9matique de France, 19 f\u00e9vrier et 12 novembre 1975"},{"key":"27_CR18","unstructured":"Souriau, J.-M.: M\u00e9canique Classique et G\u00e9om\u00e9trie Symplectique, preprint, Universit\u00e9 de Provence et Centre de Physique Th\u00e9orique (1984)"}],"container-title":["Lecture Notes in Computer Science","Geometric Science of Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-80209-7_27","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T00:05:58Z","timestamp":1626221158000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-80209-7_27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030802080","9783030802097"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-80209-7_27","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"14 July 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"GSI","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Geometric Science of Information","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Paris","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21 July 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23 July 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"gsi2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.see.asso.fr\/en\/GSI2021?screen_check=done&Width=1280&Height=720","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"125","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"98","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"78% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"The conference was held virtually.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}