Quantum statistics methods from the viewpoint of probability theory. I

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.