Intrinsic Stochasticity and Irreversibility of Classical Quantum Systems

  • M. Courbage
Part of the International Centre for Mechanical Sciences book series (CISM, volume 261)


This contribution is devoted to the question of the relation between the deterministic laws of dynamics and probabilistic descriptions of physical processes. This problem has been the object of many attempts. It is generally accepted that probabilistic processes can arise from deterministic dynamics through a process of “coarse-graining”, “contraction of the description” or by introducing extra dynamic approximations like the “molecular chaos”. In this short communication I will summarize recent results obtained by B. Misra, I. Prigogine and myself [1], [2], [3] on an alternative approach to this problem which consists in obtaining stochastic processes from deterministic dynamics by a similarity invertible linear transformations acting on the space of the distribution functions, when the dynamics is inherently random or unstable. In this case the irreversibility is obtained by a change of representation without any supplementary hypothesis.


Markov Process Semi Group Microcanonical Ensemble Inherent Randomness Probabilistic Description 
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  1. [1]
    B. Misra, I. Prigogine and M. Courbage: From deterministic dynamics to probabilistic descriptions. Proc. Natl. Acad. Sci. USA 76, p. 3607–3611, 1979 (see also Physica, to appear).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  2. [2]
    B. Misra, I. Prigogine and M. Courbage: Liapounov variable, Entropy and Measurement in Quantum Mechanics to appear in Proc. Natl. Acad. Sci.Google Scholar
  3. [3]
    M. Courbage and B. Misra: On the intrinsic randomness of classical dynamical systems to appear in J. Stat. Phys.Google Scholar
  4. [4]
    B. Misra, Proc. Natl. Acad. Sci USA 75, 1627–1631 (1978).ADSCrossRefGoogle Scholar
  5. [5]
    M. Courbage, C. Coutsomitras and B. Misra: On the of the correspondance of the deterministic dynamics and Markov processes. To appear.Google Scholar

Copyright information

© Springer-Verlag Wien 1980

Authors and Affiliations

  • M. Courbage
    • 1
  1. 1.BruxellesBelgium

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