Journal of Statistical Physics

, Volume 60, Issue 1–2, pp 281–284 | Cite as

An inequality for partition functions with disturbed Hamiltonians

  • Ch. Zylka
Short Communications


We consider a thermodynamic system consisting ofn independent subsystems. Each subsystem is described by a HamiltonianH=H0+α i H1,i=1, 2,...,n. We answer the question of how the entiretyα=(α1,α2,...,α n ) must be varied in order to change the total partition function and the total free energy of the system monotonically.

Key words

Partition function free energy inequalities majorization Schur-convex functionals 


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  1. 1.
    N. N. Bogoljubov, Jr.,Physica 32:933 (1966).Google Scholar
  2. 2.
    S. Okubo and A. Isihara,Physica 59:228 (1972).Google Scholar
  3. 3.
    A. W. Marshall and I. Olkin,Inequalities. Theory of Majorization and Its Applications (Academic Press, New York, 1979).Google Scholar
  4. 4.
    T. Ando,Majorization, Doubly Stochastic Matrices and Comparison of Eigenvalues (Hokkaido University Press, Sapporo, Japan, 1982).Google Scholar
  5. 5.
    P. M. Alberti and A. Uhlmann,Dissipative Motion in State Spaces (B. G. Teubner, Leipzig, 1981).Google Scholar
  6. 6.
    W. Thirring,Lehrbuch der Mathematischen Physik, Band 4 (Springer, Vienna, 1980).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Ch. Zylka
    • 1
  1. 1.Department of PhysicsKarl Marx UniversityLeipzigGerman Democratic Republic

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