A New Challenge for Statistical Mechanics

  • W. T. GrandyJr
Conference paper
Part of the Fundamental Theories of Physics book series (FTPH, volume 24)

Abstract

Traditionally we understand the need for probability in statistical mechanics to arise primarily from insufficient knowledge regarding initial conditions. But nonlinearities in the equations of motion can introduce irregular behavior that may lead to new phenomena, so that it is necessary to investigate how the role of probability in statistical mechanics may be affected by this observation. We conclude that the important effects are related to macroscopic equations derived from statistical mechanics.

Keywords

Statistical Mechanic Rayleigh Number Strange Attractor Macroscopic Equation Irregular Behavior 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Baskaran, Y. Fu, and P.W. Anderson: 1986, ’On the Statistical Mechanics of the Traveling Salesman Problem’ J. Stat. Phys. 45, 1.CrossRefADSMathSciNetGoogle Scholar
  2. Bender, C.M. and T.T. Wu: 1976 ’Statistical Analysis of Feynman Diagrams’ Phys. Rev. Letters 37, 117.CrossRefADSMathSciNetGoogle Scholar
  3. Grandy, W.T. Jr.: 1987, Foundations of Statistical Mechanics, Volume I: Equilibrium Theory, Redidel, DordrechtMATHGoogle Scholar
  4. Grandy, W.T. Jr.: 1988, Foundations of Statistical Mechanics, Volume II: Nonequilibrium Phenomena, Redidel, DordrechtGoogle Scholar
  5. Hénon, M. and C. Heiles: 1964, ’The Applicability of the Third Integral of the Motion: Some Numerical Experiments’ Astron J. 69, 73.CrossRefADSGoogle Scholar
  6. Hopf, E.: 1952, ’Statistical Hydromechanics and Functional Calculus’ J. Rat. Mech. Anal 1, 87.MATHMathSciNetGoogle Scholar
  7. Lorenz, E.N. 1963, ’Deterministic Nonperiodic Flows’, J. Atmos. Sci. 20, 130.CrossRefADSGoogle Scholar
  8. Lorenz, E.N. 1964 ’The Problem of Deducing the Climate from the Governing Equations’, Tellus 16, 1.CrossRefADSGoogle Scholar
  9. Saltzman, B.: 1962, ’Finite Amplitude Free Convection as an Initial Value Problem-I’, J. Atmos. Sci. 19, 329.CrossRefADSGoogle Scholar
  10. SchrÖdinger E.: 1960, Statistical Thermodynamics, Cambridge Univ. Press, Cambridge.Google Scholar
  11. Van Dyke, M.: 1982, An Album of Fluid Motion, The Parabolic Press, Stanford, CA.Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

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

Personalised recommendations