Gustavo L. Ferri

Fisher Information and Semiclassical Treatments

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.

Information, Deformed қ-Wehrl Entropies and Semiclassical Delocalization

Semiclassical delocalization in phase space constitutes a manifestation of the Uncertainty Principle, one indispensable part of the present understanding of Nature and the Wehrl entropy is widely regarded as the foremost localization-indicator. We readdress the matter here within the framework of the celebrated semiclassical Husimi distributions and their associatedWehrl entropies, suitably қ-deformed. We are able to show that it is possible to significantly improve on the extant phase-space classical-localization power.

Physical peculiarities of divergences emerging in q-deformed statistics

Abstract It was found in [A. Plastino, M.C. Rocca, Europhys. Lett. 104, 60003 (2013)] that classical Tsallis theory exhibits poles in the partition function 𝓩 and the mean energy <𝓤>. These occur at a countably set of the q-line. We give here, via a simple procedure, a mathematical account of them. Further, by focusing attention upon the pole-physics, we encounter interesting effects. In particular, for the specific heat, we uncover hidden gravitational effects.

Perturbative Treatment of the Non-Linear q-Schrödinger and q-Klein–Gordon Equations

Interesting non-linear generalization of both Schrodinger’s and Klein–Gordon’s equations have been recently advanced by Tsallis, Rego-Monteiro and Tsallis (NRT) in Nobre et al. (Phys. Rev. Lett. 2011, 106, 140601). There is much current activity going on in this area. The non-linearity is governed by a real parameter q. Empiric hints suggest that the ensuing non-linear q-Schrodinger and q-Klein–Gordon equations are a natural manifestations of very high energy phenomena, as verified by LHC-experiments. This happens for q − values close to unity (Plastino et al. (Nucl. Phys. A 2016, 955, 16–26, Nucl. Phys. A 2016, 948, 19–27)). It might thus be difficult for q-values close to unity to ascertain whether one is dealing with solutions to the ordinary Schrodinger equation (whose free particle solutions are exponentials and for which q = 1 ) or with its NRT non-linear q-generalizations, whose free particle solutions are q-exponentials. In this work, we provide a careful analysis of the q ∼ 1 instance via a perturbative analysis of the NRT equations.

Statistical, noise-related non-classicality’s indicator

Finding signs of the classical-quantum border is a very important task of perennial interest. We show, using semiclassical arguments, that the frontier between the classical and quantum domains can be characterized by recourse to idiosyncratic features of a delimiter parameter associated with the concepts of i) noise) ii) Husimi distribution functions, iii) Wherl’s entropy, and iv) escort distributions.

Deformed Generalization of the Semiclassical Entropy

We explicitly obtain here a novel expression for the semiclassical Wehrls entropy using deformed algebras built up with the qicoherent states (see Arik and Coon (J.Math.Phys. 17, 524 (1976) and Quesne (J. Phys. A 35, 9213 (2002))). The generalization is investigated with emphasis on i) its behavior as a function of temperature and ii) the results obtained when the deformation-parameter tends to unity.

Temperature effects, Frieden-Hawkins' order-measure, and Wehrl entropy

We revisit the Frieden–Hawkins’ Fisher order measure with a consideration of temperature effects. To this end, we appeal to the semiclassical approach. The order-measure’s appropriateness is validated in the semiclassical realm with regard to two physical systems. Insight is thereby gained with respect to the relationships amongst semiclassical quantifiers. In particular, it is seen that Wehrl’s entropy is as good a disorder indicator as the Frieden–Hawkins’ one.

A first order Tsallis theory

Abstract We investigate first-order approximations to both (i) Tsallis’ entropy Sq and (ii) the Sq-MaxEnt solution (called q-exponential functions eq). We use an approximation/expansion for q very close to unity. It is shown that the functions arising from the procedure (ii) are the MaxEnt solutions to the entropy emerging from (i). Our present treatment is motivated by the fact it is FREE of the poles that, for classic quadratic Hamiltonians, appear in Tsallis’ approach, as demonstrated in [A. Plastimo, M.C. Rocca, Europhys. Lett. 104, 60003 (2013)]. Additionally, we show that our treatment is compatible with extant date on the ozone layer.