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Foundations of Physics

, Volume 22, Issue 6, pp 853–866 | Cite as

On randomness and thermodynamics

  • W. T. GrandyJr.
Part II. Invited Papers Dedicated To Henry Margenau

Abstract

The past decade has witnessed significant advances in our understanding of nonlinear systems, both theoretically and experimentally. In turn, these insights have led to applications over a broad range of subjects, as well as to new interpretations of complex behavior. Inevitably, it seems, there has been a concomitant rush to re-interpret various well-understood aspects of thermodynamic behavior in manybody systems by means of these mechanisms. It is perhaps useful, therefore, to examine these notions critically, and in doing so we are able to illuminate somewhat the origins of, and motivations for, various dubious descriptions of these systems. Among other things, one notices in such discussions an unfortunate focus on “randomness,” rather than on the actual role of probabilities in describing the phenomena. Although valuable insights into some areas of complex behavior have arisen from studies of so-called “deterministic chaos,” we can detect no influence they may have on the predictions of statistical mechanics, and thus conclude that they are of little relevance to the thermodynamic behavior of large systems.

Keywords

Nonlinear System Actual Role Statistical Mechanic Valuable Insight Large System 
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.
    J. L. McCauley, “Book review,”Am. Sci., March-April, p. 167 (1990).Google Scholar
  2. 2.
    R. Pool, “Chaos theory: how big an advance?”Science 245, 26 (1989).Google Scholar
  3. 3.
    J. Ford, “HOw random is a coin toss?”Phys. Today, April, p. 40 (1983).Google Scholar
  4. 4.
    J. Ford, “What is chaos that we should be mindful of it?” in P. Davies (ed.),The New Physics (Cambridge University Press, Cambridge, 1989), p. 348.Google Scholar
  5. 5.
    J. Ford, “Chaos: solving the unsolvable, predicting the unpredictable!,” in M. F. Barnsley and S. G. Demko (eds.),Chaotic Dynamics and Fractals (Academic Press, Orlando, Florida, 1986), p. 1.Google Scholar
  6. 6.
    W. T. Grandy, Jr.,Foundations of Statistical Mechanics, Vol. II (Reidel, Dordrecht, 1988).Google Scholar
  7. 7.
    P. W. Anderson, “More is different,”Science 177, 393 (1972).Google Scholar
  8. 8.
    M. C. Mackey, “The dynamic origin of increasing entropy,”Rev. Mod. Phys. 61, 981 (1989).Google Scholar
  9. 9.
    R. Balescu,Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1975).Google Scholar
  10. 10.
    S. Smale, “On the problem of reviving the ergodic hypothesis of Boltzmann and Birkhoff,”Ann. N.Y. Acad. Sci. 357, 260 (1980).Google Scholar
  11. 11.
    A. S. Wightman, “Introduction to the problems,” in G. Velo and A. S. Wightman (eds.),Regular and Chaotic Motions in Dynamic Systems (Plenum, New York, 1985).Google Scholar
  12. 12.
    P. Gaspard and G. Nicolis, “Transport properties, Lyapunov exponents, and entropy per unit time,”Phys. Rev. Lett. 65, 1693 (1990).Google Scholar
  13. 13.
    The Random House Dictionary of the English Language (Random House, New York, 1967).Google Scholar
  14. 14.
    A. N. Kolmogorov,Foundations of the Theory of Probability (Chelsea, New York, 1950).Google Scholar
  15. 15.
    G. J. Chaitin, “Randomness and mathematical proof,”Sci. Am., May, p. 25 (1975).Google Scholar
  16. 16.
    D. R. Hofstadter,Gödel, Escher, Bach (Basic Books, New York, 1979).Google Scholar
  17. 17.
    Yu. A. Kravtsov, “Randomness, determinateness, and predictability,”Sov. Phys. Usp. 32, 434 (1989).Google Scholar
  18. 18.
    V. I. Tatarskii, “Criteria for the degree of chaos,”Sov. Phys. Usp. 32, 450 (1989).Google Scholar
  19. 19.
    E. T. Jaynes, “Probability in quantum theory,” in W. H. Zurek (ed.),Complexity, Entropy, and the Physics of Information (Addison-Wesley, Reading, Massachusetts, 1990).Google Scholar
  20. 20.
    E. T. Jaynes, “Information theory and statistical mechanics,” in K. Ford (ed.),1962 Brandeis Summer Institute in Theoretical Physics (Benjamin, New York, 1963).Google Scholar
  21. 21.
    J. W. Gibbs, “On the equilibrium of heterogeneous systems,”Trans. Conn. Acad. 3, 229 (1876).Google Scholar
  22. 22.
    W. T. Grandy, Jr.,Foundations of Statistical Mechanics, Vol. I (Reidel, Dordrecht, 1987).Google Scholar
  23. 23.
    D. J. Evans, E. G. D. Cohen, and G. P. Morriss, “Viscosity of a simple fluid from its maximal Lyapunov exponents,”Phys. Rev. A 42, 5990 (1990).Google Scholar
  24. 24.
    M. Lesieur,Turbulence in Fluids (Nijhoff, Dordrecht, 1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • W. T. GrandyJr.
    • 1
  1. 1.Department of Physics and AstronomyUniversity of WyomingLaramie

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