Abstract:
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, ultrasecond quantization, third quantization.
Citation:
V. P. Maslov, “Quantum statistics methods from the viewpoint of probability theory. I”, Teor. Veroyatnost. i Primenen., 47:4 (2002), 686–709; Theory Probab. Appl., 47:4 (2003), 665–683
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\by V.~P.~Maslov
\paper Quantum statistics methods from the viewpoint of probability theory.~I
\jour Teor. Veroyatnost. i Primenen.
\yr 2002
\vol 47
\issue 4
\pages 686--709
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\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 4
\pages 665--683
\crossref{https://doi.org/10.1137/S0040585X97980014}
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Linking options:
https://www.mathnet.ru/eng/tvp3775
https://doi.org/10.4213/tvp3775
https://www.mathnet.ru/eng/tvp/v47/i4/p686
This publication is cited in the following 3 articles:
V. P. Maslov, “Unbounded probability theory and multistep relaxation processes, II”, Math Notes, 93:5-6 (2013), 881
Maslov V.P., “Hypothetic lambda-point for noble gases”, Russian Journal of Mathematical Physics, 17:4 (2010), 454–467
V. P. Maslov, “Integral Equations and Phase Transitions in Stochastic Games. An Analogy with Statistical Physics”, Theory Probab. Appl., 48:2 (2004), 359–367
Citation in format AMSBIB
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