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Entropy2016,18, 386 32. Souriau, J.M. InterpretationGéometrique desEtatsquantiques; Springer: Berlin/Heidelberg,Germany, 1977; Volume570. (InFrench) 33. Souriau, J.M.Thermodynamiqueetgéométrie. InDifferentialGeometricalMethods inMathematicalPhysics II; Bleuler,K.,Reetz,A.,Petry,H.R.,Eds.; Springer: Berlin/Heidelberg,Germany,1978;pp.369–397. (InFrench) 34. Souriau, J.M.DynamicSystemsStructure;Chapters16–19;Unpublishedwork,1980. 35. Souriau, J.M.; Iglesias,P.HeatColdandGeometry.DifferentialGeometryandMathematicalPhysics,Mathematical PhysicsStudiesVolume; Springer:Amsterdam,TheNetherlands,1983;pp.37–68. 36. Souriau, J.M.Mécaniqueclassiqueetgéométrie symplectique.CNRSMarseille.Cent. Phys. Théor.Report ref. CPT-84/PE-16951984. (InFrench) 37. Souriau, J.M.OnGeometricMechanics.Discret. Cont.Dyn. Syst. J.2007,19, 595–607. [CrossRef] 38. Laplace,P.S.Mémoiresur laprobabilitédescausessur lesévènements. InMémoiresdeMathématiqueetde Physique;De l’ImprimerieRoyale: Paris,France,1774. (InFrench) 39. Gibbs, J.W.Elementaryprinciples in statisticalmechanics. InTheRational Foundation of Thermodynamics; Scribner:NewYork,NY,USA,1902. 40. Ruelle,D.P.ThermodynamicFormalism;Addison-Wesley:NewYork,NY,USA,1978. 41. Ruelle,D.P.Extendingthedefinitionofentropytononequilibriumsteadystates.Proc.Natl. Acad. Sci.USA 2003,100, 3054–3058. [CrossRef] [PubMed] 42. Jaynes,E.T. Informationtheoryandstatisticalmechanics.Phys. Rev. 1957,106, 620–630. [CrossRef] 43. Jaynes,E.T. Informationtheoryandstatisticalmechanics II.Phys. Rev. 1957,108, 171–190. [CrossRef] 44. Jaynes,E.T.Priorprobabilities. IEEETrans. Syst. Sci. Cybern. 1968,4, 227–241. [CrossRef] 45. Jaynes,E.T.Thewell-posedproblem.Found. Phys. 1973,3, 477–493. [CrossRef] 46. Jaynes,E.T.Wheredowestandonmaximumentropy? InTheMaximumEntropyFormalism;Levine,R.D., Tribus,M.,Eds.;MITPress:Cambridge,MA,USA,1979;pp.15–118. 47. Jaynes, E.T. Theminimumentropy production principle. Annu. Rev. Phys. Chem. 1980, 31, 579–601. [CrossRef] 48. Jaynes,E.T.Ontherationaleofmaximumentropymethods. IEEEProc. 1982,70, 939–952. [CrossRef] 49. Jaynes,E.T.PapersonProbability,Statistics andStatisticalPhysics;Reidel:Dordrecht,TheNetherlands,1982. 50. Ollivier,Y.Aspectsde l’entropie enMathématiques et enPhysique (Théoriede l’information, Systèmes Dynamiques,GrandesDéviations, Irréversibilité).Availableonline: http://www.yann-ollivier.org/entropie/ entropie.pdf (accessedon7August2015). (InFrench) 51. Villani,C. (Ir)rréversibilitéetEntropie.Availableonline: http://www.bourbaphy.fr/villani.pdf (accessedon 5August2015). (InFrench) 52. Godement,R. Introductionà laThéoriedesGroupesdeLie; Springer: Berlin/Heidelberg,Germany,2004. 53. Guichardet,A.Cohomologie desGroups Topologiques et desAlgèbres de Lie; Cedic/FernandNathan: Paris, France,1980. 54. Guichardet, A. La method des orbites: Historiques, principes, résultats. In Leçons de Mathématiques D’aujourd’hui;Cassini: Paris,France,2010;Volume4,pp.33–59. 55. Guichardet,A.LeProblèmedeKepler,Histoire etThéorie;EcolePolytechnique: Paris,France,2012. 56. Dubois, J.G.;Dufour, J.P.Lathéoriedescatastrophes.V.TransforméesdeLegendreet thermodynamique. InAnnalesde l’IHPPhysiqueThéorique; InstitutHenriPoincaré: Paris,France,1978;Volume29,pp.1–50. 57. Monge,G.Sur leCalcul IntégraldesEquationsauxDifférencesPartielles;Mémoiresde l’AcadémiedesSciences: Paris,France,1784;pp.118–192. (InFrench) 58. Moreau, J.J.Fonctionsconvexesdualesetpointsproximauxdansunespacehilbertien.C.R.Acad. Sci. 1962, 255, 2897–2899. (InFrench) 59. Plastino, A.; Plastino, A.R. On the Universality of thermodynamics’ Legendre transform structure. Phys. Lett. A1997,226, 257–263. [CrossRef] 60. Friedrich, T. Die fisher-information und symplectische strukturen. Math. Nachr. 1991, 153, 273–296. (InGerman) [CrossRef] 61. Massieu,F.Sur lesFonctionscaractéristiquesdesdiversfluides.C.R.Acad. Sci. 1869,69, 858–862. (InFrench) 62. Massieu, F.AdditionauprécédentMémoire sur lesFonctions caractéristiques. C.R.Acad. Sci. 1869, 69, 1057–1061. (InFrench) 113
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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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