Page - 113 - in Differential Geometrical Theory of Statistics
Image of the Page - 113 -
Text of the Page - 113 -
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
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