We review here the difference between quantum statistical treatments and semiclassical
ones, using as the main concomitant tool a semiclassical, shift-invariant Fisher
information measure built up with Husimi distributions. Its semiclassical character
notwithstanding, this measure also contains abundant information of a purely quantal
nature. Such a tool allows us to refine the celebrated Lieb bound for Wehrl entropies
and to discover thermodynamic-like relations that involve the degree of delocalization.
Fisher-related thermal uncertainty relations are developed and the degree of purity of
canonical distributions, regarded as mixed states, is connected to this Fisher measure
as well.
Keywords: Information theory, Semiclassical information, Fisher measures, Phase
space, Quantum distributions.
