Thermodynamic Field Theory (An Approach to Thermodynamics of Irreversible Processes)

  • Giorgio Sonnino
Part of the Nonlinear Phenomena and Complex Systems book series (NOPH, volume 9)

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.

Keywords

Field Equation Entropy Production Symmetric Tensor Thermodynamic System Straight Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Kondepudi D. and Prigogine I., Modern Thermodynamics — From Heat Engines to Dissipative Structures, (J. Wiley, New-York) 1998.MATHGoogle Scholar
  2. [2]
    Glansdorff P. and Prigogine I., Thermodynamics of Structures, Stability and Fluctuations, (John Wiley, New York) 1971.Google Scholar
  3. [3]
    Onsager L., J. Phys. Chemistry, 73 (1969) 1268.CrossRefGoogle Scholar
  4. [4]
    Schutz B., Geometrical Methods of Mathematical Physics, (Cambridge Press, Cambridge) 1980.MATHGoogle Scholar
  5. [5]
    Lovelock D. and Rund H., Tensors, Differential Forms, and Variational Principles, (Dover, New-York) 1989.Google Scholar
  6. [6]
    Prigogine I., Thermodynamics of Irreversible Processes, (J. Wiley, New-York) 1962.Google Scholar
  7. [7]
    Onsager L., Phys. Rev., 37 (1931) 405.ADSCrossRefGoogle Scholar
  8. [8]
    Onsager L., Phys. Rev., 38 (1931) 2265.ADSMATHCrossRefGoogle Scholar
  9. [9]
    Casimir H.B.J., Reviews of Modern Physics, 17 (1945) 443.ADSCrossRefGoogle Scholar
  10. [10]
    Vidal C., Dewel G and Borckmans P., Au-delà de l’équilibre, (Hermann, Éditeurs des Sciences et des Arts, Paris) 1994.Google Scholar
  11. [11]
    Synge and A. Schild, Tensor calculus, (Dover, New-York) 1969.Google Scholar
  12. [12]
    Glansdorff P. and Prigogine I., Physica, 20 (1954) 773.ADSMATHCrossRefGoogle Scholar
  13. [13]
    Einstein A., The Meaning of Relativity, (Princeton University Press, Princeton) 1956.Google Scholar
  14. [14]
    Fermi E., Sopra i Fenomeni che Avvengono in Vicinanza di una Linea Oraria, Rendiconti dei Lincei, 31 1951–1952, pp. 21–22.Google Scholar
  15. [15]
    Weyl H., Space Time Matter,(Dover Publications Inc., New-York) 1952.Google Scholar
  16. [16]
    Eisenhart L.P. Non-Riemannian Geometry, (American Mathematical Society — Colloquium Publications) 8 1927 pp.64–68.Google Scholar
  17. [17]
    Nicolis G. and Prigogine I., Self-Organisation in Nonequilibrium Systems, (Wiley, New-York) 1977.Google Scholar
  18. [18]
    Weinberg S., Gmvitation and CosmologyPrinciples and Applications of the General Theory of Relativity, (J. Wiley, New-York) 1972.Google Scholar
  19. [19]
    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.Google Scholar
  20. [20]
    Misner C. W., Thorne K.S. and Wheeler J.A., Gravitation, (W.H. Freeman and Company, San Francisco) 1973Google Scholar
  21. [21]
    Minorski N., Nonlinear Oscillations, (Van Nostrand, Princeton N.J.) 1962Google Scholar
  22. [22]
    Frankel T., The Geometry of Physics. An Introduction, (Cambridge University Press, Cambridge) 1997MATHGoogle Scholar
  23. [23]
    Nakahara M., Geometry, Topology and Physics, (lOP Publishing Ltd 1990) 1998Google Scholar
  24. [24]
    Zachmanoglou E.C. and Thoe D.W., Introduction to Partial Differential Equations with Applications, (Dover, New-York) 1986.Google Scholar
  25. [25]
    Gradshteyn I.S. and Ryzhik, Tables of Integrals, Series and Products, (Academic Press, England) 1994.Google Scholar
  26. [26]
    De Donder Th., L’Affinité, (Gauthiers-Villars, Paris) 1927.MATHGoogle Scholar
  27. [27]
    Haase. R., Thermodynamics of Irreversible Processes, (Dover Publications Inc., New-York) 1990.Google Scholar
  28. [28]
    Sonnino G., Nuovo Cimento, 115 B (2000) 1057.MathSciNetADSGoogle Scholar
  29. [29]
    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.Google Scholar
  30. [30]
    Peeters Ph. and Sonnino G., Nuovo Cimento, 115 B (2000) 1083.MathSciNetADSGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • Giorgio Sonnino
    • 1
    • 2
  1. 1.European Commission, Research Directorate-GeneralBrusselsBelgium
  2. 2.International SOLVAY Institutes of Physics and ChemistryFree University of Brussels (U.L.B.)BrusselsBelgium

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