General Equations of Motion of Statistical Physics

  • Wilhelm Brenig


The equations of motion of statistical mechanics are first-order differential equations for the evolution of statistical ensembles in time. In quantum statistics [2.1] the von Neumann equation [2.2] describes the evolution of the statistical operator; in classical statistics the Liouville equation [2.3] describes the evolution of the statistical distribution function.


Phase Space Unitary Transformation Liouville Equation Statistical Ensemble Heisenberg Picture 
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  1. 2.1
    Kadanoff, L.P., Baym, G.: Quantum Statistical Mechanics (Benjamin, New York 1962 )Google Scholar
  2. 2.2
    Neumann, J. von: Z. Phys. 57, 30 (1929)ADSCrossRefGoogle Scholar
  3. 2.3
    Liouville, J.: J. de Math. 3, 348 (1838)Google Scholar
  4. 2.4
    Brenig, W.: Statistische Theorie der Wärme I. Gleichgewicht, 2nd ed. ( Springer, Berlin, Heidelberg 1983 )Google Scholar
  5. 2.5
    Kadanoff, L.P., Martin, P.C.: Ann. Phys. 24,419 (1963). A slightly different but similar initial condition is used by Zubarev, D.N.: Nonequilibrium Thermodynamics (Consultants Bureau, New York 1974). Translation of Russian original from 1971MathSciNetADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Wilhelm Brenig
    • 1
  1. 1.Physik-DepartmentTechnische Universität MünchenGarchingFed. Rep. of Germany

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