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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.
Received: 30 October 2009; Accepted: 27 November 2009 / Published: 3 December 2009
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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MDPI and ACS Style
Pennini, F.; Ferri, G.; Plastino, A. Fisher Information and Semiclassical Treatments. Entropy 2009, 11, 972-992.
Pennini F, Ferri G, Plastino A. Fisher Information and Semiclassical Treatments. Entropy. 2009; 11(4):972-992.
Pennini, Flavia; Ferri, Gustavo; Plastino, Angelo. 2009. "Fisher Information and Semiclassical Treatments." Entropy 11, no. 4: 972-992.