Foundations of Physics

, Volume 17, Issue 9, pp 939–963 | Cite as

A fundamental link between system theory and statistical mechanics

  • H. Atmanspacher
  • H. Scheingraber


A fundamental link between system theory and statistical mechanics has been found to be established by the Kolmogorov entropy K. By this quantity the temporal evolution of dynamical systems can be classified into regular, chaotic, and stochastic processes. Since K represents a measure for the internal information creation rate of dynamical systems, it provides an approach to irreversibility. The formal relationship to statistical mechanics is derived by means of an operator formalism originally introduced by Prigogine. For a Liouville operator L and an information operator\(\tilde M\) acting on a distribution in phase space, it is shown that i[L,\(\tilde M\)]≡KI (I=identity operator). As a first consequence of this equivalence, a relation is obtained between the chaotic correlation time of a system and Prigogine's concept of a “finite duration of presence.” Finally, the existence of chaos in quantum systems is discussed with respect to the existence of a quantum mechanical time operator.


Entropy Phase Space System Theory Quantum System Temporal Evolution 
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.


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Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • H. Atmanspacher
    • 1
  • H. Scheingraber
    • 1
  1. 1.Max-Planck-Institut für Physik und Astrophysik, Institut für Extraterrestrische PhysikGarchingFRG

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