Semiclassical localization and uncertainty principle

Semiclassical localizability problems in phase space constitute a manifestation of the uncertainty principle, one of the cornerstones of our present understanding of Nature. We revisit the subject here within the framework of the celebrated semiclassical Husimi distributions and their associated Wehrl entropy. By recourse to the concept of escort distributions, a well-established statistical concept, we show that it is possible to significantly improve on the current phase-space classical-localization power, thus approaching more closely than before the bounds imposed by Husimi's thermal uncertainty relation.