The thermal statistics of quasi-probabilities in phase space

Flavia Pennini, Angel Plastino, Mario C. Rocca

Published 2014-09-15Version 1

We investigate the thermal statistics of quasi-probabilities's 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. Based on the fact that, for all of them, the Shannon entropy is a function only of the fluctuation product $\Delta x \Delta p$, we are able to ascertain that the $P$-distribution seems to becomes un-physical at very low temperatures because it would violate an analog of Heisenberg's principle in such a case. The behavior of several other information quantifiers reconfirms such an assertion in manifold ways. We also investigate the behavior of the statistical complexity and of thermal quantities like the specific heat.