636 research outputs found
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 , 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 , 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
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
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 CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - La Plata. Instituto de FĂsica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de FĂsica La Plata; Argentina. Universidad CatĂłlica del Norte. Departamento de FĂsica; ChileFil: Plastino, Ăngel Luis. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - La Plata. Instituto de FĂsica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de FĂsica La Plata; Argentin
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, -, and
Husimi's. We show that, for all of them, the ensuing semiclassical entropy is a
function {\it only} of the fluctuation product . We
ascertain that {\it the semi-classical analog of the -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
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