The thermal statistics of quasi-probabilities' analogs in phase space

TL;DR

This paper investigates the thermal properties of classical analogs of quantum phase space quasi-probabilities, revealing their entropy dependence on fluctuations and identifying unphysical behavior of the P-distribution at low temperatures.

Contribution

It provides a detailed analysis of the thermal statistics of classical analogs of quantum quasi-probabilities, highlighting their entropy dependence and the unphysical nature of the P-distribution at low temperatures.

Findings

Semiclassical entropy depends only on fluctuation product ΔxΔp.

The P-distribution becomes unphysical at very low temperatures.

Behavior of information measures and thermal quantities supports these conclusions.

Abstract

We focus attention upon the thermal statistics of the classical analogs of quasi-probabilities's (QP) in phase space for the important case of quadratic Hamiltonians. We consider the three more important OPs: 1) Wigner's, $P$-, and Husimi's. We show that, for all of them, the ensuing semiclassical entropy is a function {\it only} of the fluctuation product $\Delta x \Delta p$. We ascertain that {\it the semi-classical analog of the $P$-distribution} seems to become un-physical at very low temperatures. The behavior of several other information quantifiers reconfirms such an assertion in manifold ways. We also examine the behavior of the statistical complexity and of thermal quantities like the specific heat.