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Entropy2016,18, 386 95. DeSaxcé,G.;Vallée,C.Bargmanngroup,momentumtensorandGalilean invarianceofClausius-Duhem Inequality. Int. J.Eng. Sci. 2012,50, 216–232. [CrossRef] 96. DeSaxcé,G. Entropyand structure for the thermodynamic systems. InGeometric Science of Information, Second International Conference GSI 2015 Proceedings; Nielsen, F., Barbaresco, F., Eds.; LectureNotes in ComputerScience;Springer: Berlin/Heidelberg,Germany,2015;Volume9389,pp.519–528. 97. Kapranov,M.Thermodynamicsandthemomentmap. 2011;arXiv:1108.3472v1. 98. Pavlov,V.P.;Sergeev,V.M.Thermodynamics fromthedifferentialgeometrystandpoint.Theor.Math. Phys. 2008,157, 1484–1490. [CrossRef] 99. Cartier,P.;DeWitt-Morette,C.Functional Integration. ActionandSymmetries;CambridgeUniversityPress: Cambridge,UK,2004. 100. Libermann,P.;Marle,C.M.SymplecticGeometryandAnalyticalMechanics; SpringerScience&BusinessMedia: Berlin/Heidelberg,Germany,1987. 101. Lichnerowicz,A.EspaceshomogènesKähleriens. InColloquedeGéométrieDifférentielle;CNRSP:Paris,France, 1953;pp.171–184. (InFrench) 102. Lichnerowicz,A.ReprésentationCoadjointeQuotient etEspacesHomogènesdeContact, coursduCollègedeFrance; Springer: Berlin/Heidelberg,Germany,1986. (InFrench) 103. Balian, R.; Valentin, P.Hamiltonian structure of thermodynamicswith gauge. Eur. Phys. J. B 2001, 21, 269–282. [CrossRef] 104. Marle,C.M.OnHenriPoincaré’snote“Suruneformenouvelledeséquationsde lamécanique”. J.Geom. SymmetryPhys. 2013,29, 1–38. 105. Poincaré,H. Sur une formenouvelle des équationsde laMécanique. C.R.Acad. Sci. 1901, 7, 369–371. (InFrench) 106. Sternberg,S.Symplectichomogeneousspaces.Trans.Am.Math. Soc. 1975,212, 113–130. [CrossRef] 107. Bourguignon, J.P.CalculVariationnel;EcolePolytechnique: Paris,France,2007. (InFrench) 108. Dedecker,P.Apropertyofdifferential formsinthecalculusofvariations.Pac. J.Math. 1957,7, 1545–1549. [CrossRef] 109. Marle,C.M.Onmechanical systemswithaLiegroupasconfigurationspace. In JeanLeray ’99Conference Proceedings;DeGosson,M.,Ed.;Springer: Berlin/Heidelberg,Germany,2003;pp.183–203. 110. Marle,C.M.SymmetriesofHamiltoniansystemsonsymplecticandpoissonmanifolds. InSimilarity and SymmetryMethods; Springer: Berlin/Heidelberg,Germany,2014;pp.185–269. 111. Kirillov,A.A.Meritsanddemeritsof theorbitmethod.Bull. Am.Math. Soc. 1999,36, 433–488. [CrossRef] 112. Cartan, E. La structure des groupes de transformations continus et la théorie du trièdre mobile. Bull. Sci.Math.1910,34, 250–284. (InFrench) 113. Cartan,E.Leçons sur les Invariants Intégraux;Hermann: Paris,France,1922. (InFrench) 114. Cartan,E.Lesrécentesgénéralisationsde lanotiond’espace.Bull. Sci.Math. 1924,48, 294–320. (InFrench) 115. Cartan, E. Le rôle de la Théorie des Groupes de Lie dans L’évolution de la Géométrie Modern; C.R. Congrès International:Oslo,Norway,1936;Volume1,pp.92–103. (InFrench) 116. Libermann, P. La géométrie différentielle d’Elie Cartan à Charles Ehresmann et André Lichnerowicz. InGéométrie auXXesiècle, 1930-2000:Histoire etHorizons;Hermann: Paris,France,2005. (InFrench) 117. Koszul, J.L.Sur la formehermitiennecanoniquedesespaceshomogènescomplexes.Can. J.Math. 1955,7, 562–576. (InFrench) [CrossRef] 118. Koszul, J.L.Exposés sur lesEspacesHomogènesSymétriques;PublicaçãodaSociedadedeMatematicadeSão Paulo: SãoPaulo,Brazil, 1959. (InFrench) 119. Koszul, J.L. Domaines bornées homogènes et orbites de groupes de transformations affines. Bull. Soc. Math.Fr. 1961,89, 515–533. (InFrench) 120. Koszul, J.L.Ouverts convexes homogènes des espaces affines. Math. Z. 1962, 79, 254–259. (In French) [CrossRef] 121. Koszul, J.L.Variétés localementplatesetconvexité.Osaka J.Math. 1965,2, 285–290. (InFrench) 122. Koszul, J.L.LecturesonGroupsofTransformations;TataInstituteofFundamentalResearch: Bombay, India,1965. 123. Koszul, J.L.Déformationsdesvariétés localementplates.Ann. Inst. Fourier1968,18, 103–114. (InFrench) [CrossRef] 124. Koszul, J.L.Trajectoiresconvexesdegroupesaffinesunimodulaires. InEssaysonTopologyandRelatedTopics; Springer: Berlin,Germany,1970;pp.105–110. 115
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Differential Geometrical Theory of Statistics
Title
Differential Geometrical Theory of Statistics
Authors
Frédéric Barbaresco
Frank Nielsen
Editor
MDPI
Location
Basel
Date
2017
Language
English
License
CC BY-NC-ND 4.0
ISBN
978-3-03842-425-3
Size
17.0 x 24.4 cm
Pages
476
Keywords
Entropy, Coding Theory, Maximum entropy, Information geometry, Computational Information Geometry, Hessian Geometry, Divergence Geometry, Information topology, Cohomology, Shape Space, Statistical physics, Thermodynamics
Categories
Naturwissenschaften Physik
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