arXiv subjects

A. M. Scarfone

Publications and source records attributed to A. M. Scarfone.

At least 19 recordsLinked to original sources

arXiv2022

k-Deformed Fourier Transform

We present a new formulation of Fourier transform in the picture of the $κ$-algebra derived in the framework of the $κ$-generalized statistical mechanics. The $κ$-Fourier transform is obtained from a $κ$-Fourier series recently introduced by us [2013 Entropy {\bf15} 624]. The kernel of this transform, that reduces to the usual exponential phase in the $κ\to0$ limit, is composed by a $κ$-deformed phase and a damping factor that gives a wavelet-like behavior. We show that the $κ$-Fourier transform is isomorph to the standard Fourier transform through a changing of time and frequency variables. Nevertheless, the new formalism is useful to study, according to Fourier analysis, those functions defined in the realm of the $κ$-algebra. As a relevant application, we discuss the central limit theorem for the $κ$-sum of $n$-iterate statistically independent random variables.

cond-mat.stat-mech↗

arXiv2022

Consistency of the structure of Legendre transform in thermodynamics with the Kolmogorov-Nagumo average

We show the robustness of the structure of Legendre transform in thermodynamics against the replacement of the standard linear average with the Kolmogorov-Nagumo nonlinear average to evaluate the expectation values of the macroscopic physical observables. The consequence of this statement is twofold: 1) the relationships between the expectation values and the corresponding Lagrange multipliers still hold in the present formalism; 2) the universality of the Gibbs equation as well as other thermodynamic relations are unaffected by the structure of the average used in the theory.

cond-mat.stat-mech↗

arXiv2021

An overview of generalized entropic forms

The aim of this focus letter is to present a comprehensive classification of the main entropic forms introduced in the last fifty years in the framework of statistical physics and information theory. Most of them can be grouped into three families, characterized by two-deformation parameters, introduced respectively by Sharma, Taneja, and Mittal (entropies of degree $(α,\,β$)), by Sharma and Mittal (entropies of order $(α,\,β)$), and by Hanel and Thurner (entropies of class $(c,\,d)$). Many entropic forms examined will be characterized systematically by means of important concepts such as their axiomatic foundations {\em à la} Shannon-Khinchin and the consequent composability rule for statistically independent systems. Other critical aspects related to the Lesche stability of information measures and their consistency with the Shore-Johnson axioms will be briefly discussed on a general ground.

cond-mat.stat-mech↗

arXiv2017

Composition law of $κ$-entropy for statistically independent systems

The intriguing and still open question concerning the composition law of $κ$-entropy $S_κ(f)=\frac{1}{2κ}\sum_i (f_i^{1-κ}-f_i^{1+κ})$ with $0<κ<1$ and $\sum_i f_i =1$ is here reconsidered and solved. It is shown that, for a statistical system described by the probability distribution $f=\{ f_{ij}\}$, made up of two statistically independent subsystems, described through the probability distributions $p=\{ p_i\}$ and $q=\{ q_j\}$, respectively, with $f_{ij}=p_iq_j$, the joint entropy $S_κ(p\,q)$ can be obtained starting from the $S_κ(p)$ and $S_κ(q)$ entropies, and additionally from the entropic functionals $S_κ(p/e_κ)$ and $S_κ(q/e_κ)$, $e_κ$ being the $κ$-Napier number. The composition law of the $κ$-entropy is given in closed form, and emerges as a one-parameter generalization of the ordinary additivity law of Boltzmann-Shannon entropy recovered in the $κ\rightarrow 0$ limit.

cond-mat.stat-mech↗

arXiv2015

The role of correlation entropy in nuclear fusion in liquid lithium, indium and mercury

Nuclear fusion cross-sections considerably higher than corresponding theoretical predictions are observed in low-energy experiments with metal matrix targets and accelerated deuteron beams. The cross-section increment is significantly higher for liquid than for solid targets. We propose that the same two-body correlation entropy used in evaluating the metal melting entropy explains the large liquid-solid difference of the effective screening potential that parameterizes the cross-section increment. This approach is applied to the specific case of the $^6$Li(d,$α$)$^4$He reaction, whose measured screening potential liquid-solid difference is $(235 \pm 63)$ eV. Cross sections in the two metals with the highest two-body correlation entropy (In and Hg) have not yet been measured: increments of the cross sections in liquid relative to the ones in solid metals are estimated with the same procedure.

cond-mat.mtrl-sci↗

arXiv2014

Non-extensive thermostatistics approach to metal melting entropy

A generalized Mott relation of metal melting entropy is derived by means of non-extensive solid and liquid quantum entropy that we calculate from grand partition functions of localized ordered quantum solid and of disordered quantum Boltzmann liquid. For each of the 18 elements considered the entropic parameter $q_m$, depending on particle correlations, is deduced such that a better agreement is obtained between calculated non-extensive metal melting entropy and available experimental data. The non-extensive entropic parameter makes the difference between normal and anomalous metals. Therefore, also those not reported here should belong to one of the two classes. Possible applications to condensed matter, Earth and other solar planets seismology are mentioned.

cond-mat.stat-mech↗

arXiv2013

Entropic Forms and Related Algebras

Starting from a very general trace-form entropy, we introduce a pair of algebraic structures endowed by a generalized sum and a generalized product. These algebras form, respectively, two Abelian fields in the realm of the complex numbers isomorphic each other. We specify our results to several entropic forms related to distributions recurrently observed in social, economical, biological and physical systems including the stretched exponential, the power-law and the interpolating Bosons-Fermions distributions. Some potential applications in the study of complex systems are advanced.

math-ph↗

arXiv2011

Gauge equivalence among quantum nonlinear many body systems

Transformations performing on the dependent and/or the independent variables are an useful method used to classify PDE in class of equivalence. In this paper we consider a large class of U(1)-invariant nonlinear Schrödinger equations containing complex nonlinearities. The U(1) symmetry implies the existence of a continuity equation for the particle density $ρ\equiv|ψ|^2$ where the current ${\bfm j}_{_ψ}$ has, in general, a nonlinear structure. We introduce a nonlinear gauge transformation on the dependent variables $ρ$ and ${\bfm j}_ψ$ which changes the evolution equation in another one containing only a real nonlinearity and transforms the particle current ${\bfm j}_{_ψ}$ in the standard bilinear form. We extend the method to U(1)-invariant coupled nonlinear Schrödinger equations where the most general nonlinearity is taken into account through the sum of an Hermitian matrix and an anti-Hermitian matrix. By means of the nonlinear gauge transformation we change the nonlinear system in another one containing only a purely Hermitian nonlinearity. Finally, we consider nonlinear Schrödinger equations minimally coupled with an Abelian gauge field whose dynamics is governed, in the most general fashion, through the Maxwell-Chern-Simons equation. It is shown that the nonlinear transformation we are introducing can be applied, in this case, separately to the gauge field or to the matter field with the same final result. In conclusion, some relevant examples are presented to show the applicability of the method.

math-ph↗

arXiv2010

Intensive variables in the framework of the non-extensive thermostatistics

By assuming an appropriate energy composition law between two systems governed by the same non-extensive entropy, we revisit the definitions of temperature and pressure, arising from the zeroth principle of thermodynamics, in a manner consistent with the thermostatistics structure of the theory. We show that the definitions of these quantities are sensitive to the composition law of entropy and internal energy governing the system. In this way, we can clarify some questions raised about the possible introduction of intensive variables in the context of non-extensive statistical mechanics.

cond-mat.stat-mech↗

arXiv2009

Nonextensive relativistic nuclear and subnuclear equation of state

Following the basic prescriptions of the Tsallis' nonextensive relativistic thermodynamics, we investigate the relevance of nonextensive statistical effects on the relativistic nuclear and subnuclear equation of state. In this framework, we study the first order phase transition from hadronic to quark-gluon plasma phase by requiring the Gibbs conditions on the global conservation of the electric and the baryon charges. The relevance of small deviations from the standard extensive statistics is investigated in the context of intermediate and high energy heavy-ion collisions.

nucl-th↗

arXiv2009

Nuclear problems in astrophysical q-plasmas and environments

Experimental measurements in terrestrial laboratory, space and astrophysical observations of variation and fluctuation of nuclear decay constants, measurements of large enhancements in fusion reaction rate of deuterons implanted in metals and electron capture by nuclei in solar core indicate that these processes depend on the environment where take place and possibly also on the fluctuation of some extensive parameters and eventually on stellar energy production. Electron screening is the first important environment effect. We need to develop a treatment beyond the Debye-Huckel screening approach, commonly adopted within global thermodynamic equilibrium. Advances in the description of these processes can be obtained by means of q-thermostatistics and/or superstatistics for metastable states. This implies to handle without ambiguities the case q<1.

astro-ph.SR↗

arXiv2009

Generalized Pearson distributions for charged particles interacting with an electric and/or a magnetic field

The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to external electric and/or magnetic fields. We construct a Fokker-Planck approximation to the kinetic equations and derive the most general class of distributions for the given problem by discussing in detail some physically meaningful cases. The equivalence with the transport theory of electrons in a phonon background is also discussed.

cond-mat.stat-mech↗

arXiv2009

Asymptotic solutions of a nonlinear diffusive equation in the framework of $κ$-generalized statistical mechanics

The asymptotic behavior of a nonlinear diffusive equation obtained in the framework of the $κ$-generalized statistical mechanics is studied. The analysis based on the classical Lie symmetry shows that the $κ$-Gaussian function is not a scale invariant solution of the generalized diffusive equation. Notwithstanding, several numerical simulations, with different initial conditions, show that the solutions asymptotically approach to the $κ$-Gaussian function. Simple argument based on a time-dependent transformation performed on the related $κ$-generalized Fokker-Planck equation, supports this conclusion.

cond-mat.stat-mech↗

arXiv2008

Nuclear electron capture rate in stellar interiors and the case of 7Be

Nuclear electron capture rate from continuum in an astrophysical plasma environment (like solar core) is calculated using a modified Debye-Huckel screening potential and the related non-Gaussian q-distribution of electron momenta. For q=1 the well-known Debye-Huckel results are recovered. The value of q can be derived from the fluctuation of number of particles and temperature inside the Debye sphere. For 7Be continuum electron capture in solar core, we find an increase of 7 -- 10 percent over the rate calculated with standard Debye-Huckel potential. The consequence of this results is a reduction of the same percentage of the SSM 8B solar neutrino flux, leaving unchanged the SSM 7Be flux.

nucl-th↗

arXiv2008

Interacting particles system revisited in the framework of the q-deformed algebra

We discuss the possibility of interpreting a q-deformed non-interacting system as incorporating the effects of interactions among its particles. This can be accomplished, for instance, in an ensemble of $q$-Bosons by means of the virial expansion of a real gas in powers of the deformed parameter. The lowest order virial coefficient reduces to the case of the standard, non-interacting Bose gas, while the higher order virial coefficients contain effects arising from the interaction. The same picture can be drawn in a quantum mechanical system where it is shown that the q-deformed momentum can be expanded in a series contains high-order powers of the standard quantum phase-space variables. Motivated by this result, we introduce, in the classical framework, a transformation relating the momentum of a free system with the momentum of an interacting system. It is shown that the canonical quantization applied to the interacting system imply a q-deformed quantization for the free system.

cond-mat.stat-mech↗

arXiv2008

Analytical predictions of non-Gaussian distribution parameters for stellar plasmas

Stimulated by the recent debate on the physical relevance and on the predictivity of q-Gaussian formalism, we present specific analytical expressions for the parameters characterizing non-Gaussian distributions, such as the nonextensive parameter q, expressions that we have proposed for different physical systems, an important example being plasmas in the stellar cores.

astro-ph↗

arXiv2007

Modified Debye-Huckel Electron Shielding and Penetration Factor

Screened potential, modified by non standard electron cloud distributions responsible for the shielding effect on fusion of reacting nuclei in astrophysical plasmas, is derived. The case of clouds with depleted tails in space coordinates is discussed. The modified screened potential is obtained both from statistical mechanics arguments based on fluctuations of the inverse of the Debye-Huckel radius and from the solution of a Bernoulli equation used in generalized statistical mechanics. Plots and tables useful in evaluating penetration probability at any energy are provided.

astro-ph↗

arXiv2007

Basic-deformed thermostatistics

Starting from the basic-exponential, a q-deformed version of the exponential function established in the framework of the basic-hypergeometric series, we present a possible formulation of a generalized statistical mechanics. In a q-nonuniform lattice we introduce the basic-entropy related to the basic-exponential by means of a q-variational principle. Remarkably, this distribution exhibits a natural cut-off in the energy spectrum. This fact, already encountered in other formulations of generalized statistical mechanics, is expected to be relevant to the applications of the theory to those systems governed by long-range interactions. By employing the q-calculus, it is shown that the standard thermodynamic functional relationships are preserved, mimicking, in this way, the mathematical structure of the ordinary thermostatistics which is recovered in the q=1 limit.

cond-mat.stat-mech↗