Geodesic
Quantum statistics methods from the viewpoint of probability theory.~I
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 4, pp. 686-709

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We show that one can assign a self-adjoint operator in a Hilbert space (a symmetric matrix in the finite-dimensional case) to standard problems in probability theory and introduce the notions of entropy, temperature, and statistical ensemble. A series of general identities for these variables result, in particular, in the Bardeen–Cooper formulas for superconductivity. A rigorous proof of these asymptotics and their applications will be given in the second part of the paper.
Keywords: quantum thermodynamics, financial mathematics, third quantization.
Mots-clés : ultrasecond quantization 
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     author = {V. P. Maslov},
     title = {Quantum statistics methods from the viewpoint of probability {theory.~I}},
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V. P. Maslov. Quantum statistics methods from the viewpoint of probability theory.~I. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 4, pp. 686-709. http://geodesic.mathdoc.fr/item/TVP_2002_47_4_a3/