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

Fisher Information and Semiclassical Treatments

Flavia Pennini 1,2,* email, Gustavo Ferri 3 email and Angelo Plastino 2 email
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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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; phase space; semiclassical information; delocalization; purity; thermal uncertainties; Fisher measures

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Cite This Article

MDPI and ACS Style

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

AMA Style

Pennini F, Ferri G, Plastino A. Fisher Information and Semiclassical Treatments. Entropy. 2009; 11(4):972-992.

Chicago/Turabian Style

Pennini, Flavia; Ferri, Gustavo; Plastino, Angelo. 2009. "Fisher Information and Semiclassical Treatments." Entropy 11, no. 4: 972-992.

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