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Intrinsic randomness and intrinsic irreversibility in classical dynamical systems.

M Courbage1, I Prigogine

  • 1Faculté des Sciences, Campus Plaine Université Libre de Bruxelles, Boulevard du Triomphe, 1050 Brussels, Belgium.

Proceedings of the National Academy of Sciences of the United States of America
|April 1, 1983
PubMed
Summary

This study introduces "intrinsic irreversibility" in dynamic systems by reformulating the second law of thermodynamics. This selection rule breaks time-reversal symmetry, distinguishing possible from impossible initial conditions based on information content.

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Area of Science:

  • Statistical Mechanics
  • Dynamical Systems Theory
  • Thermodynamics

Background:

  • Previous work established methods to derive dissipative Markov processes from dynamic intrinsically random systems.
  • Unitary evolution in these systems can transform into two distinct Markov processes, leading to equilibrium at t → +∞ or t → -∞.

Purpose of the Study:

  • To lift the degeneracy between forward and backward time evolution in intrinsically random systems.
  • To formulate the second principle of thermodynamics as a selection rule applicable to these systems.
  • To establish a microscopic formulation of the second law of thermodynamics.

Main Methods:

  • Formulation of the second principle as a selection rule for intrinsically random systems.
  • Exclusion of unrealizable states based on the selection rule.

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  • Characterization of admitted initial conditions by entropy, quantifying preparation information.

    • Main Results:

    • The selection rule excludes states not invariant under velocity inversion, breaking time-reversal symmetry.
    • This results in a property termed "intrinsic irreversibility" in the dynamical systems.
    • Initial conditions selected by the second law require finite information for preparation, while rejected conditions require infinite information.

    Conclusions:

    • The proposed formulation provides a microscopic basis for the second law of thermodynamics in specific classes of dynamical systems.
    • Intrinsic irreversibility emerges from the selection rule applied to intrinsically random systems.
    • The concept of information required for state preparation is central to defining the directionality of time.