On the Increase of Entropy in the Carleman Model II

  • A. Wehrl


Statistical mechanics covers a large area within the scientific ouevre of Wolfgang Yourgrau. And perhaps the field that fascinated him most was the problem of increase of entropy and the second law of thermodynamics. Many papers as well as a wellknown textbook1 are the eloquent testimony to his preoccupation with this subject.


Boltzmann Equation Concave Function Previous Definition Hydrodynamic Limit Exceptional Point 
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.

References and Notes

  1. 1.
    W. Yourgrau, A. van der Merwe, and G. Raw, Irreversible and Statistical Thermophysics (Macmillan, New York, 1966; revised Dover edition, 1982).Google Scholar
  2. 2.
    L. Boltzmann, Wiener Berichte 66, 275 (1872).Google Scholar
  3. 3.
    G. E. Uhlenbeck, in The Boltzmann Equation ,E. G. D. Cohen and W. Thirring, editors (Springer-Verlag, Berlin, 1972).Google Scholar
  4. 4.
    H. Grad, in Handbuch der Physik ,Vol. 12, S. Flügge, editor (Springer-Verlag, Berlin, 1958).Google Scholar
  5. 5.
    O. E. Landford III, in Dynamicai Systems, Theory and Applications ,J. Moser, editor (Springer-Verlag, Berlin, 1975).Google Scholar
  6. 6.
    O. E. Landford III, in International Conference on Dynamical Systems in Mathematical Physics ,Soc. Mathèmatique de France, Astèrisque 40, 1975.Google Scholar
  7. 7.
    H. Spohn, Rev. Mod. Phys. ,52, 569 (1980).CrossRefGoogle Scholar
  8. 8.
    C. Cercignani, Theory and Application of the Boltzmann Equation (Scottish Acad. Pr., Edinburgh, 1975).Google Scholar
  9. 9.
    T. Carleman, Problémes Mathèmatiques dans la Th é orie Cinétique des Gaz (Almqvist and Wiksell, Uppsala, 1957).Google Scholar
  10. 10.
    H. Kaper and G. K. Leaf, “Initial Value Problems for the Carleman Equation,” preprint, Argonne, 1979.Google Scholar
  11. 11.
    A. Wehrl and W. Yourgrau, Phys. Lett. 72A, 13 (1979).Google Scholar
  12. 12.
    A. Wehrl, Found. Phys. 9, 939 (1979).CrossRefGoogle Scholar
  13. 13.
    I. Csiszar, Stud. Sci. Math. Hung. 2, 299 (1967).Google Scholar
  14. 14.
    A. Renyi, Wahrscheinlichkeitsrechnung (Deutscher Verlag der Wissenschaften, Berlin, 1961).Google Scholar
  15. 15.
    W. Thirring, Lehrbuch der mathematischen Physik ,Vol. 4 (Springer-Verlag, Vienna, to appear).Google Scholar
  16. 16.
    A. Wehrl, Rev. Mod. Phys. 50, 221 (1978).CrossRefGoogle Scholar
  17. 17.
    A. Uhlmann, Wiss. Z. Karl-Marx-Univ. Leipzig, Math.-Naturw. R. 20, 633 (1971); 21, 427 (1972); 22, 139 (1973).Google Scholar
  18. 18.
    A. Wehrl, Rep. Math. Phys. 6, 15 (1974).CrossRefGoogle Scholar
  19. 19.
    E. Ruch, Theor. Chim. Acta 38, 167 (1975).CrossRefGoogle Scholar
  20. 20.
    E. Ruch and A. Mead, Theor. Chim. Acta 41, 95 (1976).CrossRefGoogle Scholar
  21. 21.
    A. Uhlmann, Rostocker Physikalische Manuskripte 2, 45 (1977).Google Scholar
  22. 22.
    A. Wehrl, in Recent Advances in Statistical Mechanics ,A. Corciovei, editor (Central Institute of Physics, Bucharest, 1980).Google Scholar
  23. 23.
    B. Crell, T. de Paly, and A. Uhlmann, Wiss. Z. Karl-Marx-Univ. Leipzig, Math.-Naturw. R. 27, 229 (1978).Google Scholar
  24. 24.
    B. Crell and A. Uhlmann, preprint KMU-QFT-3, Leipzig, 1979.Google Scholar
  25. 25.
    L. Tartar, in Dynamical Systems ,Vol. l, L. Cesari et al. ,editors (Academic Press, New York, 1976).Google Scholar
  26. 26.
    G. H. Hardy, J. E. Littlewood, and G. Polya, Jnequaiities (Cambridge Univ. Press, Cambridge, 1934).Google Scholar
  27. 27.
    F. Riesz and B. Sz.-Nagy, Vorlesungen über Funktionalanalysis (Deutscher Verlag der Wissenschaften, Berlin, 1956).Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • A. Wehrl
    • 1
  1. 1.Institut für Theoretische PhysikUniversität WienViennaAustria

Personalised recommendations