. Dans-cette-annexe, nous fournissons un formulaire des mod eles thermodynamiques que nous avons retrouv e a vec ! . Pour chaque mod ele, nous donnons 1. L'hamiltonien de contact utilis e, 2. Le champ de contact associ e, 3. Les equations d' etat calcul ees, 4. Les fonctions thermodynamiques A; H; G; z, 5

. Esp and . Qu, il n'y a pas d'erreurs. Nous rappelons, de plus, dans ce formulaire les dii erents hamiltoniens de contact que nous avons d etermin es

J. E. Abraham and . Mardsen, Foundations of mechanics, 1967.

B. C. Adachi and . Lu, Simplest equation of state for vapor-liquid equilibrium calculation ; a modiication of the van der waals equation, AIChE J, vol.30, p.9911993, 1984.

I. Arnold, M ethodes math ematiques de la m ecanique classique, 1976.

I. Arnold, Contact geometry and wave propagation. Lectures given at the University of Oxford in November and December 1988 under the sponsorship of the International Mathematical Union, Serie des Conferences de l'Union Mathematique Internationale, 1989.

I. Arnold, Contact geometry and wave propagation, Enseign. Math II, Ser, vol.36, issue.334, p.2155266, 1990.

I. Arnold, Contact geometry, Proceeding of the Gibbs Symposium, Proc. Symp. Occas. J. W. Gibbs 150th Anniv, p.1633179, 1989.
DOI : 10.1007/978-94-011-3330-2_3

I. Arnold and S. P. , Dynamical Systems IV, 1985.
DOI : 10.1007/978-3-662-06791-8

I. Arnold, A. Varchenho, and S. Goussein-zad, Singularit es des applications dii erentiables, 1986.

I. Arnold, A. N. Varchenko, A. B. Givental, and A. G. Khovanskij, Singularities of functions, wave fronts, caustics and multidimensional integrals, Sov. Sci. Rev., Sect. C, Math. Phys., Rev, vol.4, p.1192, 1984.

S. Bamberg and . Sternberg, A c ourse in mathematics for students of physics 2, 1990.

E. Blair, Contact manifolds in Riemannian Geometry, 1976.
DOI : 10.1007/BFb0079307

L. Burke, Applied diierential geometry. Cambridge etc, 1985.

. Caratheodory, Calculus of variations and partial diierential equations of the rst order, 1965.

. Cartan, Sur certaines expressions dii erentielles et le probl eme de pfaa, p.2399332, 1899.
DOI : 10.24033/asens.467
URL : http://archive.numdam.org/article/ASENS_1899_3_16__239_0.pdf

E. Cartan, Lecons sur les invariants integraux, 1971.

H. Cartan, Cours de calcul dii erentiel, 1967.

. Cerf, Transformations de contact et Probl emes de Pfaa, 1929.

C. Chao and R. A. Greenkorn, Thermodynamics of uids, 1975.

C. D. De-verdi-ere, A g eom etrie symplectique, Institut Fourier, 1982.

R. Courant and . Hilbert, Methods of mathematical physics. I n terscience publishers, 1962.

G. Edelen, Applied Exterior Calculus, 1985.

. Emanuel, Advanced Classical Thermodynamics AIAA education series, 1988.
DOI : 10.2514/4.861291

. Favard, Cours de g eom etrie dii erentielle locale, 1957.

. Flanders, Diierential Forms with Applications to the Physical Sciences. D o ver publication inc, 1989.

T. Fomenko, Symplectic geometry. Gordon and Breach Science Publishers, 1988.

W. Gibbs, The Collected Works of J. Willard Gibbs, Volume I Thermodynamics, 1948.

. Gilmore, Catastrophe theory for scientists and engineers. A Wiley-Interscience Publication, 1981.

. Gray, Some Global Properties of Contact Structures, The Annals of Mathematics, vol.69, issue.2, p.4211450, 1959.
DOI : 10.2307/1970192

. Grmela, Thermodynamical lift of the nonlinear onsager-casimir vector eld In Hamiltonian systems, transformation groups and spectral methods, 1990.

V. Guillemin and . Sternberg, Symplectic techniques in physics, 1984.

R. Hermann, Geometry,Physics,and Systems, 1973.

R. Janyszek and . Mrugala, Geometrical structure of the state space in classical statistical and phenomenological thermodynamics, Reports on Mathematical Physics, vol.27, issue.2, pp.1455-159, 1989.
DOI : 10.1016/0034-4877(89)90001-3

. Jost, Riemannian Geometry and Geometric Analysis, 1995.

. Jurkowski, The inverse problem for a linear vector eld in thermodynamics, Rep.Math.Phys, vol.41, 1998.

. Jurkowski, Continuous contact transformations and the meaning of contact hamiltonian, preprint, 1999.

S. Kobayashi and . Nomizu, Foundations of diierential geometry. I n terscience publishers, 1963.

. Lee and M. Kesler, A generalized thermodynamic correlation based on threeparameter correspondind states, AiChE Journal, vol.213, p.5100527, 1975.

P. Libermann, Sur les automorphismes innntesimaux des structures symplectiques et des structures de contact, Centre Belge Rech math ,Colloque Geom. dif. globale, 1959.

P. Libermann, Cartan-darboux theorems for pfaaan forms on foliated manifolds, diierential geometry, Proc. 6th Int. Colloq. santiago de CompostellaaSpain, 1989.

. Libermann, Legendre foliations on contact manifolds, Differential Geometry and its Applications, vol.1, issue.1, p.57776, 1991.
DOI : 10.1016/0926-2245(91)90022-2

C. M. Libermann and . Marle, Symplectic Geometry and Analytical Mechanics, 1987.
DOI : 10.1007/978-94-009-3807-6

. Macutan, Geometry of diierential equations and formal inegrability theory, Laboratoire de Mod elisation et Calcul, 1997.

. Mrugala, Submanifolds in the thermodynamic phase space, Reports on Mathematical Physics, vol.21, issue.2, 1985.
DOI : 10.1016/0034-4877(85)90059-X

. Mrugala, Continuous contact transformations in thermodynamics, Reports on Mathematical Physics, vol.33, issue.1-2, p.1499154, 1993.
DOI : 10.1016/0034-4877(93)90050-O

. Mrugala, Lie, jacobi, poisson and quasi-poisson structures in thermodynamics, p.37745, 1995.

J. D. Mrugala, J. C. Nulton, P. Schoen, and . Salamon, Contact structure in thermodynamic theory, Reports on Mathematical Physics, vol.29, issue.1, p.1099121, 1991.
DOI : 10.1016/0034-4877(91)90017-H

. Olver, Applications of Lie Groups to Diierential Equations, 1986.

S. Omohundro, Geometric Pertubation Theory in Physics, W orld Scientiic, 1986.

. Parisse, Cours de g eom etrie dii erentielle et symplectique. Cours de l' ecole d' et e de l'Institut Fourier, 1995.

P. Eneloux, E. Rauzy, and R. Freze, A consistent v olume correction for redlichkwong-soave v olumes, Fluid Phase Equilibria, vol.8, p.7723, 1982.

L. Reinhart, Diierential Geometry of Foliations, 1983.

. Sasaki, On diierentiable manifolds with certain structures wich are closely related to almost contact structure, T^ ohoku Math, 1960.

H. Schmidt and . Wenzel, A modiied van der waals type equation of state, Chem. Eng. Science, vol.35, p.150331512, 1980.

J. Sewell, Maximum and minimum principles. A uniied approach, with applications . Cambridge Texts in Applied Mathematics, 1987.
DOI : 10.1017/cbo9780511569234

W. Sharpe, Diierential Geometry, 1997.

. Soave, Improvement of the Van Der Waals equation of state, Chemical Engineering Science, vol.39, issue.2, p.3577369, 1984.
DOI : 10.1016/0009-2509(84)80034-2

. Spivak, A c omprehensive introduction to diierential geometry, 1979.

A. Vassilyev, Lagrange and Legendre characteristic classes, 1988.