Journal of Statistical Physics

, Volume 25, Issue 1, pp 111–126 | Cite as

On intrinsic randomness of dynamical systems

  • S. Goldstein
  • B. Misra
  • M. Courbage


We discuss the problem of nonunitary equivalence, via positivity-preserving similarity transformations, between the unitary groups associated with deterministic dynamical evolution and semigroups associated with stochastic processes. Dynamical systems admitting such nonunitary equivalence with stochastic Markov processes are said to beintrinsically random. In a previous work, it was found that the so-called Bernoulli systems (discrete time) are intrinsically random in this sense. This result is extended here by showing that a more general class of dynamical systems—the so-calledK systems andK flows—are intrinsically random. The connection of intrinsic randomness with local instability of motion is briefly discussed. We also show that Markov processes associated through nonunitary equivalence tononisomorphic K flows are necessarily non-isomorphic.

Key words

Dynamical systems Markov processes K flows H theorem time operator irreversibility instability 


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Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • S. Goldstein
    • 1
  • B. Misra
    • 2
  • M. Courbage
    • 2
  1. 1.Department of MathematicsRutgers UniversityNew Brunswick
  2. 2.Faculté des SciencesUniversité Libre de BruxellesBrusselsBelgium

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