Abstract
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.
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References
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Lenard, A. Thermodynamical proof of the Gibbs formula for elementary quantum systems. J Stat Phys 19, 575–586 (1978). https://doi.org/10.1007/BF01011769
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DOI: https://doi.org/10.1007/BF01011769