Fisher information and semiclassical reatments

FLAVIA PENNINI; GUSTAVO FERRI; ANGELO PLASTINO

ENTROPY

Molecular Diversity Preservation International (MDPI)

Año: 2009 vol. 11 p. 972 - 992

1099-4300

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.