Concepts and Recent Advances in Generalized Information Measures and Statistics

1. Since the introduction of the information measure widely known as Shannon entropy, quantifiers based on information theory and concepts such as entropic forms and statistical complexities have ...
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Semiclassical Treatments and Information Theory

Pp. 256-282 (27)

Flavia Pennini, Angelo Plastino and Gustavo Luis Ferri

Abstract

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.

Affiliation:

Departamento de Fisica, Universidad Catolica del Norte, Av. Angamos 0610, Antofagasta, Chile