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

Fisher Information and Semiclassical Treatments

1,2,* , 3
 and 2
Received: 30 October 2009; Accepted: 27 November 2009 / Published: 3 December 2009
(This article belongs to the Special Issue Maximum Entropy)
Download PDF [266 KB, uploaded 4 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 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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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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