Abstract
The thermodynamic field theory (TFT) allows to deal with thermodynamic systems submitted even to strong non-equilibrium conditions. The theory herein formulated enables to find field equations whose solutions give the generalised relations between the thermodynamic forces and their conjugated flows. It will be shown that evolution of the thermodynamic systems is well described in the Weyl’s space. In the particular case in which the thermodynamic forces and conjugated flows are linked only through a symmetric tensor (the metric tensor), the resulting geometry is the Riemannian geometry. As example of application, the thermoelectric effect and the unimolecular triangular chemical reaction are analysed in great detail.
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References
Kondepudi D. and Prigogine I., Modern Thermodynamics — From Heat Engines to Dissipative Structures, (J. Wiley, New-York) 1998.
Glansdorff P. and Prigogine I., Thermodynamics of Structures, Stability and Fluctuations, (John Wiley, New York) 1971.
Onsager L., J. Phys. Chemistry, 73 (1969) 1268.
Schutz B., Geometrical Methods of Mathematical Physics, (Cambridge Press, Cambridge) 1980.
Lovelock D. and Rund H., Tensors, Differential Forms, and Variational Principles, (Dover, New-York) 1989.
Prigogine I., Thermodynamics of Irreversible Processes, (J. Wiley, New-York) 1962.
Onsager L., Phys. Rev., 37 (1931) 405.
Onsager L., Phys. Rev., 38 (1931) 2265.
Casimir H.B.J., Reviews of Modern Physics, 17 (1945) 443.
Vidal C., Dewel G and Borckmans P., Au-delà de l’équilibre, (Hermann, Éditeurs des Sciences et des Arts, Paris) 1994.
Synge and A. Schild, Tensor calculus, (Dover, New-York) 1969.
Glansdorff P. and Prigogine I., Physica, 20 (1954) 773.
Einstein A., The Meaning of Relativity, (Princeton University Press, Princeton) 1956.
Fermi E., Sopra i Fenomeni che Avvengono in Vicinanza di una Linea Oraria, Rendiconti dei Lincei, 31 1951–1952, pp. 21–22.
Weyl H., Space Time Matter,(Dover Publications Inc., New-York) 1952.
Eisenhart L.P. Non-Riemannian Geometry, (American Mathematical Society — Colloquium Publications) 8 1927 pp.64–68.
Nicolis G. and Prigogine I., Self-Organisation in Nonequilibrium Systems, (Wiley, New-York) 1977.
Weinberg S., Gmvitation and Cosmology —Principles and Applications of the General Theory of Relativity, (J. Wiley, New-York) 1972.
Feynman R.P., Gauge Theories, Les Houches, Session XXIX, 1976 — Weak and electromagnetic interactions at high energy, (R. Balian and C.H. Llewellyn Smith eds., Amsterdam: North-Holland Publishing Company) 1977.
Misner C. W., Thorne K.S. and Wheeler J.A., Gravitation, (W.H. Freeman and Company, San Francisco) 1973
Minorski N., Nonlinear Oscillations, (Van Nostrand, Princeton N.J.) 1962
Frankel T., The Geometry of Physics. An Introduction, (Cambridge University Press, Cambridge) 1997
Nakahara M., Geometry, Topology and Physics, (lOP Publishing Ltd 1990) 1998
Zachmanoglou E.C. and Thoe D.W., Introduction to Partial Differential Equations with Applications, (Dover, New-York) 1986.
Gradshteyn I.S. and Ryzhik, Tables of Integrals, Series and Products, (Academic Press, England) 1994.
De Donder Th., L’Affinité, (Gauthiers-Villars, Paris) 1927.
Haase. R., Thermodynamics of Irreversible Processes, (Dover Publications Inc., New-York) 1990.
Sonnino G., Nuovo Cimento, 115 B (2000) 1057.
Ferziger J.H. and Kaper H.G., Mathematical Theory of Transport Processes in Gases, (North-Holland, Amsterdam and American Elsevier Publishing Company, New-York) 1956.
Peeters Ph. and Sonnino G., Nuovo Cimento, 115 B (2000) 1083.
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Sonnino, G. (2004). Thermodynamic Field Theory (An Approach to Thermodynamics of Irreversible Processes). In: Descalzi, O., MartÃnez, J., Rica, S. (eds) Instabilities and Nonequilibrium Structures IX. Nonlinear Phenomena and Complex Systems, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0991-1_20
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DOI: https://doi.org/10.1007/978-94-007-0991-1_20
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