Journal of Statistical Physics

, Volume 19, Issue 6, pp 575–586 | Cite as

Thermodynamical proof of the Gibbs formula for elementary quantum systems

  • A. Lenard


An elementary derivation is given of the formula for the thermal equilibrium states of quantum systems that can be described in finite-dimensional Hilbert spaces. The three assumptions made, Passivity, Structural Stability, and Consistency, have phenomenological interpretations. Except at zero temperature, Structural Stability follows already from Passivity and a weak form of Consistency.

Key words

Statistical mechanics thermal equilibrium Gibbs states 


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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • A. Lenard
    • 1
  1. 1.Departments of Mathematics and PhysicsIndiana UniversityBloomington

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