Classical thermodynamics from quasi-probabilities

Abstract

The basic idea of a microscopic understanding of thermodynamics is to derive its main features from a microscopic probability distribution. In such a vein, we investigate the thermal statistics of quasi-probabilities’s semiclassical analogs in phase space for the important case of quadratic Hamiltonians, focusing attention in the three more important instances, i.e. those of Wigner, [Formula: see text]- and Husimi distributions. Introduction of an effective temperature permits one to obtain a unified thermodynamic description that encompasses and unifies the three different quasi-probability distributions. This unified description turns out to be classical.