Page - 112 - in Differential Geometrical Theory of Statistics

Entropy2016,18, 386 3. Barbaresco,F.Symplectic structureof informationgeometry: FishermetricandEuler-Poincaréequationof souriau liegroupthermodynamics. InGeometricScienceof Information,Second InternationalConferenceGSI 2015;Nielsen,F.,Barbaresco,F.,Eds.;Springer: Berlin/Heidelberg,Germany,2015;Volume9389,pp.529–540. 4. DeSaxcé,G.;Vallée,C.GalileanMechanicsandThermodynamicsofContinua;Wiley-ISTE:London,UK,2016. 5. Vallée,C.Relativistic thermodynamicsofcontinua. Int. J.Eng. Sci. 1981,19, 589–601. [CrossRef] 6. Vallée,C.;Lerintiu,C.Convexanalysisandentropycalculation instatisticalmechanics.Proc.ARazmadze Math. Inst. 2005,137, 111–129. 7. Marle, C.M. FromTools in Symplectic and PoissonGeometry to J.-M. Souriau’s Theories of Statistical MechanicsandThermodynamics.Entropy2016,18, 370. [CrossRef] 8. DeSaxcé,G.Linkbetweenliegroupstatisticalmechanicsandthermodynamicsofcontinua. InSpecial Issue MDPIEntropy“DifferentialGeometricalTheoryofStatistics”;MDPI:Basel,Switzerland,2016;Volume18,p.254. 9. Barbaresco, F. Koszul information geometry and souriau geometric temperature/capacity of lie group thermodynamics.Entropy2014,16, 4521–4565. [CrossRef] 10. Souriau, J.M.StructuredesSystèmesDynamiques;Editions JacquesGabay: Paris,France,1970. (InFrench) 11. Souriau, J.M.StructureofDynamicalSystems,volume149ofProgress inMathematics. InASymplecticView ofPhysics;Birkhäuser: Basel,Switzerland,1997. 12. Nielsen,F.;Barbaresco,F.GeometricScienceof Information; Springer: Berlin/Heidelberg,Germany,2015. 13. Kosmann-Schwarzbach,Y.LagéométriedePoisson, créationduXXièmesiècle. InSiméon-DenisPoisson; EcolePolytechnique: Paris,France,2013;pp.129–172. 14. Bismut, J.M.MécaniqueAléatoire; Springer: Berlin/Heidelberg,Germany,1981;Volume866. 15. Casas-Vázquez, J.; Jou,D.Temperature innon-equilibriumstates:Areviewofopenproblemsandcurrent proposals.Rep. Prog. Phys. 2003,66, 1937–2023. [CrossRef] 16. Streater,R.F.The informationmanifoldforrelativelyboundedpotentials.Tr.Mat. Inst. Steklova2000,228, 217–235. 17. Arnold,V.I. Sur lagéométriedifférentielledesgroupesdeLiededimension infinie et ses applicationsà l’hydrodynamiquedesfluidesparfaits.Ann. Inst. Fourier1966,16, 319–361. [CrossRef] 18. Arnold, V.I.; Givental, A.B. Symplectic geometry. InDynamical Systems IV: Symplectic Geometry and Its Applications, Encyclopaedia of Mathematical Sciences; Arnol’d, V.I., Novikov, S.P., Eds.; Springer: Berlin, Germany,1990;Volume4,pp.1–136. 19. Marle, C.M.; de Saxcé, G.; Vallée, C. L’oeuvre de Jean-Marie Souriau, Gazette de la SMF,Hommage à Jean-MarieSouriau. 2012. PublishedbySMF,Paris. 20. Patrick Iglesias, Itinéraired’unMathématicien:UnentretienAvec Jean-MarieSouriau,Le JournaldeMaths desElèves.Availableonline: http://www.lutecium.fr/jp-petit/science/gal_port/interview_Souriau.pdf (accessedon27October2016). (InFrench) 21. Iglesias,P.Symétries etMoment;Hermann: Paris,France,2000. 22. Kosmann-Schwarzbach,Y.Groupes etSymmetries;EcolePolytechnique: Paris,France,2006. 23. Kosmann-Schwarzbach,Y.EnhomageàJean-MarieSouriau,quelquessouvenirs.GazettedesMathématiciens 2012,133, 105–106. 24. Ghys,E.Actions localement libresdugroupeaffine. Invent.Math. 1985,82, 479–526. [CrossRef] 25. Rais,M.La representationcoadjointedugroupeaffine. Ann. Inst. Fourier1978,28, 207–237. (InFrench) [CrossRef] 26. Souriau, J.M.Mécaniquedesétatscondensésde lamatière. InProceedingsof the1st InternationalSeminar ofMechanicsFederationofGrenoble,Grenoble,France,19–21May1992. (InFrench) 27. Souriau, J.M.Géométriede l’espacedephases.Commun.Math. Phys. 1966,374, 1–30. (InFrench) 28. Souriau, J.M.Définition covariante des équilibres thermodynamiques. NuovoCimento 1966, 1, 203–216. (InFrench) 29. Souriau, J.M.MécaniqueStatistique,GroupesdeLie etCosmologie;Colloques InternationauxduCNRSNuméro 237: Paris,France,1974;pp.59–113. (InFrench) 30. Souriau, J.M.Géométrie Symplectique et PhysiqueMathématique; ÉditionsduC.N.R.S.: Paris, France, 1975. (InFrench) 31. Souriau, J.M.ThermodynamiqueRelativistedesFluides;CentredePhysiqueThéorique:Marseille,France,1977. (InFrench) 112