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Foundations of Physics

, Volume 5, Issue 4, pp 573–589 | Cite as

Thermodynamics of averaged motion

  • B. H. Lavenda
Article
  • 57 Downloads

Abstract

The thermodynamics of averaged motion treats the asymptotic spatiotemporal evolution of nonlinear irreversible processes. Dissipative and conservative actions are associated with short and long spatiotemporal scales, respectively. The motion of asymptotically stable systems is slow, monotonic, and continuous, so that the microscopic state variable description of rapid motion can be supplanted by an analysis of the macroscopic variable equations of motion of amplitude and phase. Rapid motion is associated with instability, and the direction of system motion is determined by thermodynamic criteria, in place of an analysis of the microscopic equations of motion. The characteristic structural configurations, deduced from the extremum principles of partial differential equations, are compared with the thermodynamic criteria. As a result of the nature of asymptotic motion, variational principles exist which characterize the asymptotic states of the system.

Keywords

Differential Equation Partial Differential Equation Variational Principle Stable System Variable Equation 
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.
    B. H. Lavenda,Lett. Nuovo Cimento 10, 385 (1972); to appear inFound. Phys. Google Scholar
  2. 2.
    N. Minorsky,Nonlinear Oscillations (Van Nostrand, New York, 1962).Google Scholar
  3. 3.
    A. A. Andronov, A. A. Vitt, and S. E. Khaikin,Theory of Oscillators (Pergamon Press, London, 1966).Google Scholar
  4. 4.
    B. H. Lavenda,Found. Phys. 3, 53 (1973).Google Scholar
  5. 5.
    S. Chapman and T. G. Cowling,The Mathematical Theory of Non-Uniform Gases (Cambridge Univ. Press, 1952).Google Scholar
  6. 6.
    G. Whitham,Proc. Roy. Soc. A 283, 238 (1965),J. Fluid Mech. 44, 373 (1970).Google Scholar
  7. 7.
    I. M. Gel'fand,Usp. Mat. Nauk (N. S.) 14, 87 (1959).Google Scholar
  8. 8.
    R. Courant and K. O. Friedrich,Supersonic Flow and Shock Waves (Interscience, New York, 1948).Google Scholar
  9. 9.
    A. Blaquière,Nonlinear System Analysis (Academic Press, New York, 1962).Google Scholar
  10. 10.
    M. H. Protter and H. F. Weinberger,Maximum Principles in Differential Equations (Prentice Hall, Englewood Cliffs, New Jersey, 1967).Google Scholar
  11. 11.
    B. H. Lavenda,Found. Phys. 2(2/3), 161 (1972).Google Scholar
  12. 12.
    S. Machlup and L. Onsager,Phys. Rev. 91, 1512 (1953).Google Scholar
  13. 13.
    B. H. Lavenda,Phys. Rev. A 9, 929 (1974).Google Scholar
  14. 14.
    Lord Rayleigh,Theory of Sound (Dover, New York, 1945).Google Scholar
  15. 15.
    L. Onsager,Phys. Rev. 37, 405 (1931).Google Scholar
  16. 16.
    L. Onsager and S. Machlup,Phys. Rev. 91, 1505 (1953).Google Scholar
  17. 17.
    L. D. Landau and E. M. Lifshitz,Fluid Mechanics (Pergamon Press, London, 1959).Google Scholar
  18. 18.
    A. Katchalsky and P. F. Curran,Nonequilibrium Thermodynamics in Biophysics (Harvard Univ. Press, Cambridge, 1967).Google Scholar
  19. 19.
    R. Courant and D. Hilbert,Methods of Mathematical Physics (Interscience, New York, 1962), Vol. II.Google Scholar
  20. 20.
    E. Hopf,Proc. Am. Math. Soc. 3, 791 (1952).Google Scholar
  21. 21.
    I. Prigogine,Irreversible Thermodynamics (Interscience, New York, 1967).Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • B. H. Lavenda
    • 1
  1. 1.International Institute of Genetics and BiophysicsNaplesItaly

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