Quantumness' Degree of Thermal Optics' Approximations

We assess the degree of quantumness of the P, Q, and W quantum optics' approximations in a thermal context governed by the canonical ensemble treatment. First, we remint the reader of the bridge connecting quantum optics with statistical mechanics using the abovementioned approximations at the temperature T. With the ensuing materials, we explore with some detail some features of the above bridge, related to the entropy and to thermal uncertainties. Some new relations concerning the degree of quantumness of the P, Q, and W are obtained by comparison between them and the exact and classical treatments.