Approach and Return to Equilibrium

  • Heide Narnhofer
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 11/1973)


In Thermodynamics we work with thermodynamical ensembles, for the infinite system we speak of equilibrium states. For a well behaving system we hope, starting with a state not too wild, that after a sufficiently long time the results of measurements should equal the results of measurements in an equilibrium state. This can mean mathematically either that the state tends weakly to the equilibrium state or that the mean in time of the state exists and that the time of recurrence is small in comparison to the time the measurement takes.


Invariant State Thermal Bath Free Fermion Gibbs State Finite System 
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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  1. 1.
    D. Ruelle, Statistical Mechanics, Benjamin 1969.Google Scholar
  2. 2.
    J. Dixmier, Les Algèbres d’Operateurs dans l’Espace Hilbertien, Gauthier Villars 1957.Google Scholar
  3. 3.
    J. Dixmier, Les C*-Algèbres, Gauthier Villars 1964.Google Scholar
  4. 4.
    G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, New York 1972.Google Scholar
  5. 5.
    H. Narnhofer, Acta Phys. Austr. 31, 349 (1970).MathSciNetGoogle Scholar
  6. 6.
    W. Thirring and A. Wehrl, Comm. Math. Phys. 4, 303 (1967).CrossRefMATHADSMathSciNetGoogle Scholar
  7. 7.
    W. Thirring, Comm. Math. Phys. 7, 181 (1968).CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    F. Jelinek, Comm. Math. Phys. 9, 169 (1968).CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    W. Thirring in L.M. Garrido, A. Cruz, T.W. Preist, The Many Body Problem, Plenum Press, London 1969.Google Scholar
  10. 10.
    D. Dubin, G. L. Sewell, J. Math. Phys. 11, 2990 (1970).CrossRefMATHADSMathSciNetGoogle Scholar
  11. 11.
    D. Ruelle, Hely. Phys. Acta 45, 215 (1972).Google Scholar
  12. 12.
    H. Narnhofer, Acta Phys. Austr. 36, 217 (1972).MathSciNetGoogle Scholar
  13. 13.
    O. E. Lanford, D. W. Robinson, Comm. Math. Phys. 24, 193 (1972).CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    H. Narnhofer, W. Thirring and R. Sexl, Ann. of Phys. 57/2 351 (1970).Google Scholar
  15. 15.
    J. Manuceau, F. Rocca, D. Testard, Comm. Math. Phys. 12, 43 (1969).CrossRefMATHADSMathSciNetGoogle Scholar
  16. 16.
    C. Radin, J. Math. Phys. 11, 2945 (1970).CrossRefADSMathSciNetGoogle Scholar
  17. 17.
    H. Araki, H. Mijata, Publ. Res. Inst. Math. Sci., Kyoto Univ., ser. A 4, 373 (1968).MATHGoogle Scholar
  18. 18.
    D. W. Robinson, preprint, Marseille 1972.Google Scholar
  19. 19.
    H. Porta, J. T. Schwartz, Comm. on Pure and Appl. Math., 20, 457 (1967).MATHMathSciNetGoogle Scholar
  20. 20.
    K. Hepp, Hely. Phys. Acta 45, 237 (1972).Google Scholar
  21. 21.
    A. López, Z. f. Physik 192/1, 63 (1966).Google Scholar
  22. 22.
    E. Presutti, E. Scacciatelli, G. L. Sewell, F. Wanderlingh, J. Math. Phys. 13, 1085 (1972).CrossRefADSMathSciNetGoogle Scholar
  23. 23.
    C. Radin, Comm. Math. Phys. 21, 291 (1971).Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Heide Narnhofer
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of ViennaAustria

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