On Boltzmann Entropy and Coarse — Graining for Classical Dynamical Systems

  • Maurice Courbage
Part of the NATO ASI Series book series (NSSB, volume 256)


We discuss a possible construction of Markov evolutions with Boltzmann entropy, associated, through a coarse — graining, to deterministic systems which are not as strongly unstable as K — systems. Yet, this extension implies that the dynamical system should have an absolutely continuous component in its spectrum.


Kolmogorov Equation Continuous Component Boltzmann Entropy Classical Dynamical System Uncountable Number 
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  1. 1.
    B. Misra, I. Prigogine, and M. Courbage. Physica 98 A, 1 (1979).MathSciNetCrossRefGoogle Scholar
  2. 2.
    B. Misra and I. Prigogine. Suppl. Prog. Theor. Phys. 69, 101 (1980).MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    M. Courbage and G. Nicolis. Europhys. Lett. 11, 1 (1990).ADSCrossRefGoogle Scholar
  4. 4.
    K. Yosida. Functional Analysis. Springer, Berlin, 1965.MATHGoogle Scholar
  5. 5.
    S. Goldstein, B. Misra, and M. Courbage. J. Stat. Phys. 25, 111 (1980).MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    F.R. Gantmacher. Théorie des Matrices, Vol.2. Dunod, Paris, 1966.MATHGoogle Scholar
  7. 7.
    J. Mathew and M.G. Nadkarni. Bull. London Math. Soc. 11, 402 (1984).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Maurice Courbage
    • 1
  1. 1.Laboratoire de ProbabilitésUniversité Pierre et Marie Curie CNRSParisFrance

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