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Entropy 2009, 11(4), 972-992; doi:10.3390/e11040972

Fisher Information and Semiclassical Treatments

1,2,* , 3
1 Departamento de Física, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta, Chile 2 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 3 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.
Received: 30 October 2009 / Accepted: 27 November 2009 / Published: 3 December 2009
(This article belongs to the Special Issue Maximum Entropy)
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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; phase space; semiclassical information; delocalization; purity; thermal uncertainties; Fisher measures information theory; phase space; semiclassical information; delocalization; purity; thermal uncertainties; Fisher measures
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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

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