{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T15:45:17Z","timestamp":1747237517376,"version":"3.40.3"},"publisher-location":"Cham","reference-count":12,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030269791"},{"type":"electronic","value":"9783030269807"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-26980-7_25","type":"book-chapter","created":{"date-parts":[[2019,8,18]],"date-time":"2019-08-18T23:03:04Z","timestamp":1566169384000},"page":"239-247","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Expectation Variables on a Para-Contact Metric Manifold Exactly Derived from Master Equations"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5249-1054","authenticated-orcid":false,"given":"Shin-itiro","family":"Goto","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6405-4361","authenticated-orcid":false,"given":"Hideitsu","family":"Hino","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,8,2]]},"reference":[{"key":"25_CR1","volume-title":"Methods of Information Geometry. AMS","author":"S Amari","year":"2000","unstructured":"Amari, S., Nagaoka, H.: Methods of Information Geometry. AMS. Oxford University Press, Oxford (2000)"},{"key":"25_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-56478-4","volume-title":"Information Geometry","author":"N Ay","year":"2017","unstructured":"Ay, N., et al.: Information Geometry. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-56478-4"},{"key":"25_CR3","doi-asserted-by":"publisher","first-page":"073301","DOI":"10.1063\/1.4927226","volume":"56","author":"S Goto","year":"2015","unstructured":"Goto, S.: Legendre submanifolds in contact manifolds as attractors and geometric nonequilibrium thermodynamics. J. Math. Phys. 56, 073301 (2015). [30 pages]","journal-title":"J. Math. Phys."},{"key":"25_CR4","doi-asserted-by":"publisher","first-page":"102702","DOI":"10.1063\/1.4964751","volume":"57","author":"S Goto","year":"2016","unstructured":"Goto, S.: Contact geometric descriptions of vector fields on dually flat spaces and their applications in electric circuit models and nonequilibrium thermodynamics. J. Math. Phys. 57, 102702 (2016). [40 pages]","journal-title":"J. Math. Phys."},{"key":"25_CR5","doi-asserted-by":"publisher","first-page":"125206","DOI":"10.1088\/1751-8113\/48\/12\/125206","volume":"48","author":"A Bravetti","year":"2015","unstructured":"Bravetti, A., Lopez-Monsalvo, C.S.: Para-Sasakian geometry in thermodynamic fluctuation theory. J. Phys. A: Math. Theor. 48, 125206 (2015). [21 pages]","journal-title":"J. Phys. A: Math. Theor."},{"key":"25_CR6","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1016\/j.aop.2015.07.010","volume":"361","author":"A Bravetti","year":"2015","unstructured":"Bravetti, A., Lopez-Monsalve, C.S., Nettel, F.: Contact symmetries and Hamiltonian thermodynamics. Ann. Phys. 361, 377\u2013400 (2015)","journal-title":"Ann. Phys."},{"key":"25_CR7","unstructured":"Goto, S., Hino, H.: Information and contact geometric description of expectation variables exactly derived from master equations. arXiv:1805.10592v2"},{"key":"25_CR8","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s10455-008-9147-3","volume":"36","author":"S Zamkovoy","year":"2009","unstructured":"Zamkovoy, S.: Canonical connections on paracontact manifolds. Ann. Glob. Geom. 36, 37\u201360 (2009)","journal-title":"Ann. Glob. Geom."},{"key":"25_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-45330-7","volume-title":"Lectures on Symplectic Geometry","author":"AC da Silva","year":"2008","unstructured":"da Silva, A.C.: Lectures on Symplectic Geometry, 2nd edn. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-45330-7","edition":"2"},{"key":"25_CR10","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1016\/0034-4877(78)90010-1","volume":"14","author":"R Mrugala","year":"1978","unstructured":"Mrugala, R.: Geometrical formulation of equilibrium phenomenological thermodynamics. Rep. Math. Phys. 14, 419\u2013427 (1978)","journal-title":"Rep. Math. Phys."},{"key":"25_CR11","doi-asserted-by":"publisher","first-page":"3156","DOI":"10.1103\/PhysRevA.41.3156","volume":"41","author":"R Mrugala","year":"1990","unstructured":"Mrugala, R.: Statistical approach to the geometric structure of thermodynamics. Phys. Rev. A 41, 3156\u20133160 (1990)","journal-title":"Phys. Rev. A"},{"key":"25_CR12","first-page":"167","volume":"1142","author":"R Mrugala","year":"2000","unstructured":"Mrugala, R.: On contact and metric structures on thermodynamic spaces. Suken kokyuroku 1142, 167\u2013181 (2000)","journal-title":"Suken kokyuroku"}],"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\/978-3-030-26980-7_25","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,12]],"date-time":"2024-03-12T18:03:41Z","timestamp":1710266621000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-26980-7_25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030269791","9783030269807"],"references-count":12,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-26980-7_25","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"2 August 2019","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":"Toulouse","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":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 August 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29 August 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"gsi2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.see.asso.fr\/GSI2019","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}