Classical thermodynamics from quasi-probabilities

Abstract

The basic idea of a microscopic understanding of thermodynamics is to derive its mainfeatures from a microscopic probability distribution. In such a vein, we investigate thethermal statistics of quasi-probabilities?s semiclassical analogs in phase space for theimportant case of quadratic Hamiltonians, focusing attention in the three more importantinstances, i.e. those of Wigner, P- and Husimi distributions. Introduction of aneffective temperature permits one to obtain a unified thermodynamic description thatencompasses and unifies the three different quasi-probability distributions. This unifieddescription turns out to be classical.