Quantum statistical information contained in a semi-classical Fisher--Husimi measure

We study here the difference between quantum statistical treatments and semi-classical ones, using as the main research tool a semi-classical, shift-invariant Fisher information measure built up with Husimi distributions. Its semi-classical character notwithstanding, this measure also contains 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.Comment: 9 pages, 3 figures; chenged conten

Heisenberg-Fisher thermal uncertainty measure

With the help of the coherent states' basis we establish an interesting connection among i) the so-called Wehrl entropy, ii) Fisher's information measure $I$, and iii) the canonical ensemble entropy for the one-dimensional quantum harmonic oscillator (HO). We show that the contribution of the excited HO spectrum to the mean thermal energy is given by $I$, while the pertinent canonical partition function is given by another Fisher measure: the so-called shift invariant one, minus the HO's ground state energy. Our findings should be of interest in view of the fact that it has been shown that the Legendre transform structure of thermodynamics can be replicated without any change if one replaces the Boltzmann-Gibbs-Shannon entropy by Fisher's information measure [{\it Physical Review E} {\bf 60}, 48 (1999)]. New Fisher-related uncertainty relations are also advanced.Comment: Physical Review E (2004), in pres

Tsallis' entropy maximization procedure revisited

The proper way of averaging is an important question with regards to Tsallis' Thermostatistics. Three different procedures have been thus far employed in the pertinent literature. The third one, i.e., the Tsallis-Mendes-Plastino (TMP) normalization procedure, exhibits clear advantages with respect to earlier ones. In this work, we advance a distinct (from the TMP-one) way of handling the Lagrange multipliers involved in the extremization process that leads to Tsallis' statistical operator. It is seen that the new approach considerably simplifies the pertinent analysis without losing the beautiful properties of the Tsallis-Mendes-Plastino formalism.Comment: 17 pages, no figure

Fluctuations, entropic quantifiers and classical-quantum transition

We show that a special entropic quantifier, called the statistical complexity, becomes maximal at the transition between super-Poisson and sub-Poisson regimes. This acquires important connotations given the fact that these regimes are usually associated with, respectively, classical and quantum processes.Fil: Pennini, Flavia Catalina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Universidad Católica del Norte. Departamento de Física; ChileFil: Plastino, Ángel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin

Power-Law distributions and Fisher's information measure

We show that thermodynamic uncertainties (TU) it preserve their form in passing from Boltzmann-Gibbs' statistics to Tsallis' one provided that we express these TU in terms of the appropriate variable conjugate to the temperature in a nonextensive context.Comment: accepted for publication in Physica

The thermal statistics of quasi-probabilities' analogs in phase space

We focus attention upon the thermal statistics of the classical analogs of quasi-probabilities's (QP) in phase space for the important case of quadratic Hamiltonians. We consider the three more important OPs: 1) Wigner's, $P$-, and Husimi's. We show that, for all of them, the ensuing semiclassical entropy is a function {\it only} of the fluctuation product $\Delta x \Delta p$. We ascertain that {\it the semi-classical analog of the $P$-distribution} seems to become un-physical at very low temperatures. The behavior of several other information quantifiers reconfirms such an assertion in manifold ways. We also examine the behavior of the statistical complexity and of thermal quantities like the specific heat.Comment: 11 pages, 6 figures.Text has change

Naudts-like duality and the extreme Fisher information principle

We show that using the most parsimonious version of Frieden and Soffer's extreme information principle (EPI) with a Fisher measure constructed with escort probabilities, the concomitant solutions obey a type of Naudts' duality for nonextensive ensembles. We also determine in closed form the general (normalized) probability distribution that minimizes Fisher's information.Comment: 4 pages, no figure