Non-equilibrium Variational Principles

  • Bernard H. Lavenda


Thermodynamic variational principles offer both a unification and classification of the fundamental laws governing non-equilibrium processes. At the heart of all thermodynamic variational principles is the principle of least dissipation of energy (Onsager, 1931). As a result of Onsager’s formulation of the principle of least dissipation of energy, the dissipation function has, by far, a more prominent and respectable role in thermodynamic variational principles than it has in the variational principles of mechanics (Routh, 1877).


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  1. Casimir, H. B. G. (1945). On Onsager’s principle of microscopic reversibility. Rev. mod. Phys., 17, 343–350.CrossRefGoogle Scholar
  2. Glansdorff, P. and Prigogine, I. (1964). On a general evolution criterion in macroscopic physics. Physica, 30, 351–374.CrossRefGoogle Scholar
  3. Gyarmati, I. (1965a). Zsurn. Fiz. Himii (Moscow) T., 39, 1489. Gyarmati, I. (1965b). Acta. Chim. Hung., 43, 353.Google Scholar
  4. Gyarmati, I. (1965c). Periodica Polytech., 9, 205.Google Scholar
  5. Gyarmati, I. (1966). Acta. Chim. Hung., 47, 63.Google Scholar
  6. Gyarmati, I. (1970). Non-Equilibrium Thermodynamics. Springer-Verlag, Berlin.CrossRefGoogle Scholar
  7. Kirkaldy, J. S. (1964). Can. J. Phys., 42, 1447.CrossRefGoogle Scholar
  8. Lavenda, B. H. (1972). Concepts of stability and symmetry in irreversible thermodynamics I. Found. Phys., 2, 161–179.CrossRefGoogle Scholar
  9. Lavenda, B. H. (1974). Principles and representations of nonequilibrium thermodynamics. Phys. Rev. A, 9, 929–943.CrossRefGoogle Scholar
  10. Lavenda, B. H. (1977). The path integral formulation of nonequilibrium statistical mechanics. La Rivista del Nuovo Cimento, 7, 229–276.CrossRefGoogle Scholar
  11. Machlup, S. and Onsager, L. (1953). Fluctuations and irreversible processes. II. Systems with kinetic energy. Phys. Rev., 91, 1512–1515.CrossRefGoogle Scholar
  12. Ono, S. (1961). Variational principles in thermodynamics and statistical mechanics of irreversible processes, Advan. Chem. Phys., 3, 267–321.Google Scholar
  13. Onsager, L. (1931). Reciprocal relations in irreversible processes I. Phys. Rev., 37, 405–426; Reciprocal relations in irreversible processes II. Phys. Rev., 38, 2265–2279.CrossRefGoogle Scholar
  14. Onsager, L. and Machlup, S. (1953). Fluctuations and irreversible processes. Phys. Rev., 91, 1505–1512.CrossRefGoogle Scholar
  15. Prigogine, I. (1954). Bull. Acad. Roy. Belg. Cl. Sci., 31, 600.Google Scholar
  16. Prigogine, I. (1965). Non-Equilibrium Thermodynamics, Variational Techniques, and Stability. (Eds. Donnelly, R., Herman, R. and Prigogine I.), Chicago University Press, Chicago.Google Scholar
  17. Rayleigh, Lord (J. W. Strutt) (1873). Proc. Lond. math. Soc., 4, 357.Google Scholar
  18. Routh, E. J. (1877). A Treatise on the Stability of a Given State of the Motion. Macmillan, London.Google Scholar
  19. Tisza, L. and Manning, I. (1957). Fluctuations and irreversible thermodynamics. Phys. Rev., 105, 1695–1705.CrossRefGoogle Scholar

General references on variational principles

  1. Lanczos, C. (1949). The Variational Principles of Mechanics. University of Toronto Press, Toronto.Google Scholar
  2. Yourgrau, W. and Mandelstam, S. (1960). Variational Principles in Dynamics and Quantum Theory, 2 ed. Pitman, London.Google Scholar

Copyright information

© Bernard H. Lavenda 1978

Authors and Affiliations

  • Bernard H. Lavenda
    • 1
  1. 1.Istituto di Fisica Sperimentale della Facoltà di ScienzeUniversità di NapoliItaly

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