Intrinsic Irreversibility in Classical and Quantum Mechanics

  • I. E. Antoniou
  • I. Prigogine
Conference paper
Part of the Fundamental Theories of Physics book series (FTPH, volume 24)


Intrinsically Irreversible Dynamical Systems allow for an exact passage to Irreversible Evolution through appropriate non-Unitary change of Representation. The property which characterises such systems is Dynamical Instability expressed by the Kolmogorov Partition and Internal Time or by the non-vanishing of the asymptotic Collision Operator. This leads to an extension of both Classical and Quantum Mechanics. Certain implications of the Kolmogorov Instability and Internal Time for Relativistic Systems as well as of the non-vanishing of the asymptotic Collision Operator for Unstable quantum systems are discussed.


Lamb Shift Internal Time Past Light Cone Dynamics Entropy Irreversible 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Schrodinger E. (1944) ’The statistical law in nature’ Nature 152, 704ADSCrossRefGoogle Scholar
  2. 2.
    Prigogine I. (1980) From being to becoming ,Freeman.Google Scholar
  3. 3.
    Misra B. (1978) ’Non equilibrium entropy, Liapunov variables and ergodic properties of classical systems’ P.N.A.S. U.S.A. 75, 1627CrossRefGoogle Scholar
  4. 4.
    Misra B., Prigogine I., Courbage M. (1979) ’Liapounov variable,entropy and measurement in quantum mechanics’ P.N.A.S. U.S.A. 76, 4768MathSciNetCrossRefGoogle Scholar
  5. 5.
    Misra B., Prigogine I. (1983) ’Irreversibility and non- locality’ Lett. Math. Phys. 1 421ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Misra B., Prigogine I., Courbage M. (1979) ’From deterministic dynamics to probabilistic descriptions’ Physica 98A, 1ADSMathSciNetGoogle Scholar
  7. 7.
    Misra B., Prigogine I. (1982) ’Time, Probability and Dynamics’ in Long Time Predictions in Dynamic Systems ed. by Horton E.W. et als, Wiley N.Y.Google Scholar
  8. 8.
    Goodrich R. K., Gustafson K., Misra B. (1986) ’On K -Flows and Irreversibility’ J. Stat. Phys. 42 317ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    GLockhart C. Misra B. (1986) ’Irreversibility and Measurement in Quantum Mechanics’ Physica 136A 47ADSMathSciNetGoogle Scholar
  10. 10.
    Misra B. (1987) ’Fields as Kolmogorov flows’ J. Stat. Phys. 48 1295ADSCrossRefGoogle Scholar
  11. 11.
    Antoniou I.E. (1988) Internal Time and Irreversibility of Relativistic Dynamical Systems , Thesis Free University of Brussels.Google Scholar
  12. 12.
    Antoniou I.E. ,Misra B. to appearGoogle Scholar
  13. 13.
    Lax P. Phillips R. (1967) Scattering Theory Academic PressGoogle Scholar
  14. 14.
    Poincare H. (1892) Les Methods Nouvelles de la Mecanique Celeste Dover Reprint 1957Google Scholar
  15. 15.
    Petrosky T. Prigogine I. (1988) ’Poincare’s theorem and Unitary transformations for classical and quantum theory’ Physica 147A 459ADSGoogle Scholar
  16. 16.
    Prigogine I. 1962 Non Equilibrium Statistical Mechanic WileyGoogle Scholar
  17. 17.
    Prigogine I., George C., Henin F., Rosenfield L. 1973 A unified formulation of Dynamics and Thermodynamics Chem. Scr. 4 5Google Scholar
  18. 18.
    George C., Mayne F., Prigogine I. (1985) ’Scattering theory in superspace’ ,in Adv. Chem.Phys . 61 ,WileyGoogle Scholar
  19. 19.
    Prigogine I. Petrosky T. 1987 ’Intrinsic Irreversibility in quantum theory’ Physica 142A 33ADSGoogle Scholar
  20. 20.
    Prigogine I. Petrosky T. (1988) ’An alternative to quantum theory’ Physica 142A 461ADSMathSciNetGoogle Scholar
  21. 21.
    Lighthill J. (1986) ’The recently recognized failure of predictability in Newtonian Dynamics’ Proc. R. Soc. London A407 35ADSGoogle Scholar
  22. 22.
    Popper K. (1982) Quantum theory and the schism in Physic from the Postscript to the Logic of the scientific discovery Rowman and Littlefield, OtowaGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • I. E. Antoniou
    • 1
  • I. Prigogine
    • 2
  1. 1.Faculté des Sciences ,CP 231Université Libre des BruxellesBruxellesBelgium
  2. 2.Center for Studies in Statistical MechanicsThe University of Texas at AustinAustinUSA

Personalised recommendations