Classical thermodynamics from quasi-probabilities

TL;DR

This paper explores how classical thermodynamics can be derived from semi-classical phase space quasi-probabilities, unifying different distributions through an effective temperature in a classical framework.

Contribution

It introduces a unified thermodynamic description based on quasi-probabilities in phase space, applicable to Wigner, P-, and Husimi distributions for quadratic Hamiltonians.

Findings

Unified classical thermodynamics from quasi-probabilities

Effective temperature links different phase space distributions

The approach applies to quadratic Hamiltonians

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 semi-classical analogs in phase space for the important case of quadratic Hamiltonians, focusing attention in the three more important instances, i.e., those of Wigner, $P$-, 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.