Skip to main content
Log in

Concepts of stability and symmetry in irreversible thermodynamics. I

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

Concepts of stability and symmetry in irreversible thermodynamics are developed through the analysis of system energy flows. The excess power function, derived from a local energy conservation equation, is shown to yield necessary and sufficient stability criteria for linear and nonlinear irreversible processes. In the absence of symmetry-destroying external forces, the linear range may be characterized by a set of phenomenological coefficient symmetries relating coupled forces and displacements, velocities, and accelerations, whereas rotational phenomena in nonlinear processes may be characterized by skew-symmetric components of the phenomenological coefficients. A physical interpretation of the nature of the skew-symmetric parts is given and the variational principle of minimum dissipation of energy is related to a stability criterion.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. A. Guillemin,Introductory Circuit Theory (Wiley, New York, 1953), Chapters 7 and 10.

    Google Scholar 

  2. B. H. Lavenda,Foundations of Physics, to appear.

  3. L. Onsager,Phys. Rev. 37, 405 (1931);38, 2265 (1931).

    Google Scholar 

  4. I. Prigogine and R. Balescu,Bull. Classe Sci. Acad. Roy. Belg. 41, 912 (1955);42, 256 (1956).

    Google Scholar 

  5. J. W. Strutt (Lord Rayleigh),Theory of Sound (Dover, New York, 1945), pp. 150–157.

    Google Scholar 

  6. E. J. Routh,A Treatise on the Stability of a Given State of Motion (MacMillan and Co., London, 1877), Chapter 4.

    Google Scholar 

  7. L. D. Landau and E. M. Lifshitz,Statistical Physics (Pergamon Press, London, 1959), p. 58.

    Google Scholar 

  8. L. Onsager and S. Machlup,Phys. Rev. 91, 1505 (1953).

    Google Scholar 

  9. S. Machlup and L. Onsager,Phys. Rev. 91, 1512 (1953).

    Google Scholar 

  10. P. Glansdorff and I. Prigogine,Physica 20, 773 (1954).

    Google Scholar 

  11. H. C. Mel,Bull. Classe Sci. Acad. Roy. Belg. 40, 839 (1954).

    Google Scholar 

  12. E. J. Routh,Dynamics of a System of Rigid Bodies, Part II (Dover, New York, 1955).

    Google Scholar 

  13. P. Glansdorff and I. Prigogine,Physica 30, 351 (1964);31, 1242 (1965). P. Glansdorff and I. Prigogine,Thermodynamic Theory of Structure, Stability and Fluctuations (Interscience, New York, 1971).

    Google Scholar 

  14. B. H. Lavenda,Prog. Theor. Phys., to appear.

  15. A. J. Lotka,Proc. Natl. Acad. Sci. (U.S.) 8, 146 (1922).

    Google Scholar 

  16. A. Gray,A Treatise on Gyrostatics and Rotational Motion (Dover, New York, 1959), p. 416.

    Google Scholar 

  17. I. Prigogine,Introduction to Thermodynamics of Irreversible Processes (Wiley, New York, 1967), p. 112.

    Google Scholar 

  18. W. Thomson and P. G. Tait,Treatise on Natural Philosophy (Cambridge Univ. Press, Cambridge, 1886), p. 393.

    Google Scholar 

  19. B. H. Lavenda, Thesis Université Libre de Bruxelles, Bruxelles, Belgium, 1970.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lavenda, B.H. Concepts of stability and symmetry in irreversible thermodynamics. I. Found Phys 2, 161–179 (1972). https://doi.org/10.1007/BF00708499

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00708499

Keywords

Navigation