  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.
