Ergodic properties of infinite systems

  • Sheldon Goldstein
  • Joel L. Lebowitz
  • Michael Aizenman
I. Statistical Mechanics
Part of the Lecture Notes in Physics book series (LNP, volume 38)


Macroscopic systems are successfully modeled in statistical mechanics, at least in equilibrium, by infinite systems. We discuss the ergodic theoretic structure of such systems and present results on the ergodic properties of some simple model systems. We argue that these properties, suitably refined by the inclusion of space translations and other structure, are important for an understanding of the nonequilibrium properties of macroscopic systems.


Infinite System Finite System Ergodic Property Origin Event Macroscopic System 
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  1. [1]
    Lebowitz, J. L., and Penrose, O., Physics Today, Vol. 26, No. 2 (1973).Google Scholar
  2. [2]
    Ornstein, D. S., Ergodic Theory, Randomness, and Dynamical Systems, in New Haven: Yale University Press, 1974; see also his contributions in this volume.Google Scholar
  3. [3]
    Goldstein, S., Occupation number measures and the uniqueness of the state in classical statistical mechanics (to appear).Google Scholar
  4. [4]
    Goldstein, S., and Lebowitz, J. L., Commun. Math. Phys. 37, 1 (1974).Google Scholar
  5. [5]
    Sinai, Y. G., Funkts. Analiz. 6, 1 (1972) 41.Google Scholar
  6. [6]
    Aizenmann, M., Goldstein, S., and Lebowitz, J. L., Ergodic properties of a one-dimensional system of hard rods with an infinite number of degrees of freedom, Commun. Math. Phys., 39, 289 (1975).Google Scholar
  7. [7]
    Shields, P., The theory of Bernoulli shifts, University of Chicago Press (1973).Google Scholar
  8. [8]
    Pazzis, O., de, Commun. Math. Phys. 22 (1971) 121.Google Scholar
  9. [9]
    Katznelson, Y., and Weiss, B., Israel S. Math. 12 (1972) 161.Google Scholar
  10. [10]
    Conze, J. P., Z. Wahrscheinlichkeitstheorie verw. Geb. 25 (1972) 11–30.Google Scholar
  11. [11]
    Goldstein, S., Space-time ergodic properties of systems of infinitely many independent particles, Commun. Math. Phys., 39, 303 (1975).Google Scholar
  12. [12]
    Parry, W., Entropy and generators in ergodic theory, New York: Benjamin (1969).Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Sheldon Goldstein
    • 1
  • Joel L. Lebowitz
    • 2
  • Michael Aizenman
    • 2
  1. 1.Institute for Advanced StudyPrinceton University
  2. 2.Belfer Graduate School of ScienceYeshiva University

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