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Fisher Information and Semiclassical Treatments

Departamento de Física, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta, Chile
Instituto de Física La Plata (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata (UNLP), Consejo Nacional de Investigaciones (CCT-CONICET), C.C. 727, (1900) La Plata, Argentina
Facultad de Ciencias Exactas y Naturales, Universidad Nacional de La Pampa, Uruguay 151, Santa Rosa, La Pampa, Argentina
Author to whom correspondence should be addressed.
Entropy 2009, 11(4), 972-992;
Received: 30 October 2009 / Accepted: 27 November 2009 / Published: 3 December 2009
(This article belongs to the Special Issue Maximum Entropy)
PDF [266 KB, uploaded 24 February 2015]


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. View Full-Text
Keywords: information theory; phase space; semiclassical information; delocalization; purity; thermal uncertainties; Fisher measures information theory; phase space; semiclassical information; delocalization; purity; thermal uncertainties; Fisher measures

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Pennini, F.; Ferri, G.; Plastino, A. Fisher Information and Semiclassical Treatments. Entropy 2009, 11, 972-992.

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