arXiv subjects

A. M. Scarfone

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

At least 37 records · Page 2Linked to original sources

arXiv2007

Equivalence among different formalisms in the Tsallis entropy framework

In a recent paper [Phys. Lett. A {\bf335}, 351 (2005)] the authors discussed the equivalence among the various probability distribution functions of a system in equilibrium in the Tsallis entropy framework. In the present letter we extend these results to a system which is out of equilibrium and evolves to a stationary state according to a nonlinear Fokker-Planck equation. By means of time-scale conversion, it is shown that there exists a ``correspondence'' among the self-similar solutions of the nonlinear Fokker-Planck equations associated with the different Tsallis formalisms. The time-scale conversion is related to the corresponding Lyapunov functions of the respective nonlinear Fokker-Planck equations.

cond-mat.stat-mech↗

arXiv2007

Stochastic quantization of interacting classical particles system

Starting from a many-body classical system governed by a trace-form entropy we derive, in the stochastic quantization picture, a family of non linear and non-Hermitian Schroedinger equations describing, in the mean filed approximation, a quantum system of interacting particles. The time evolution of the main physical observables is analyzed by means of the Ehrenfest equations showing that, in general, this family of equations takes into account dissipative and damped effects due to the interaction of the system with the background. We explore the presence of steady states by means of solitons, describing conservative solutions. The results are specialized to the case of a system governed by the Boltzmann-Gibbs entropy.

cond-mat.stat-mech↗

arXiv2006

A mechanism to derive multi-power law functions: an application in the econophysics framework

It is generally recognized that economical systems, and more in general complex systems, are characterized by power law distributions. Sometime, these distributions show a changing of the slope in the tail so that, more appropriately, they show a multi-power law behavior. We present a method to derive analytically a two-power law distribution starting from a single power law function recently obtained, in the frameworks of the generalized statistical mechanics based on the Sharma-Taneja-Mittal information measure. In order to test the method, we fit the cumulative distribution of personal income and gross domestic production of several countries, obtaining a good agreement for a wide range of data.

physics.data-an↗

arXiv2006

Classical and quantum q-deformed physical systems

On the basis of the non-commutative q-calculus, we investigate a q-deformation of the classical Poisson bracket in order to formulate a generalized q-deformed dynamics in the classical regime. The obtained q-deformed Poisson bracket appears invariant under the action of the q-symplectic group of transformations. In this framework we introduce the q-deformed Hamilton's equations and we derive the evolution equation for some simple q-deformed mechanical systems governed by a scalar potential dependent only on the coordinate variable. It appears that the q-deformed Hamiltonian, which is the generator of the equation of motion, is generally not conserved in time but, in correspondence, a new constant of motion is generated. Finally, by following the standard canonical quantization rule, we compare the well known q-deformed Heisenberg algebra with the algebra generated by the q-deformed Poisson bracket.

quant-ph↗

arXiv2006

Thermal and mechanical equilibrium among weakly interacting systems in generalized thermostatistics framework

We consider two statistically independent systems described by the same entropy belonging to the two-parameter family of Sharma-Mittal. Assuming a weak interaction among the systems, allowing in this way an exchange of heat and work, we analyze, both in the entropy representation and in the energy representation, the evolution toward the equilibrium. The thermodynamics evolution is controlled by two scalar quantities identified with the temperature and the pressure of the system. The thermodynamical stability conditions of the equilibrium state are analyzed in both representations. Their relationship with the concavity conditions for the entropy and with the convexity conditions for the energy are spotlighted.

cond-mat.stat-mech↗

arXiv2005

Dissociative attachment of an electron to a molecule: kinetic theory

Test particles interact with a medium by means of a bimolecular reversible chemical reaction. Two species are assumed to be much more numerous so that they are distributed according fixed distributions: Maxwellians and Dirac's deltas. Equilibrium and its stability are investigated in the first case. For the second case, a system is constructed, in view of an approximate solution.

cond-mat.stat-mech↗

arXiv2005

Legendre structure of the thermostatistics theory based on the Sharma-Taneja-Mittal entropy

The statistical proprieties of complex systems can differ deeply for those of classical systems governed by Boltzmann-Gibbs entropy. In particular, the probability distribution function observed in several complex systems shows a power law behavior in the tail which disagrees with the standard exponential behavior showed by Gibbs distribution. Recently, a two-parameter deformed family of entropies, previously introduced by Sharma, Taneja and Mittal (STM), has been reconsidered in the statistical mechanics framework. Any entropy belonging to this family admits a probability distribution function with an asymptotic power law behavior. In the present work we investigate the Legendre structure of the thermostatistics theory based on this family of entropies. We introduce some generalized thermodynamical potentials, study their relationships with the entropy and discuss their main proprieties. Specialization of the results to some one-parameter entropies belonging to the STM family are presented.

cond-mat.stat-mech↗

arXiv2005

Classical q-deformed dynamics

On the basis of the quantum q-oscillator algebra in the framework of quantum groups and non-commutative q-differential calculus, we investigate a possible q-deformation of the classical Poisson bracket in order to extend a generalized q-deformed dynamics in the classical regime. In this framework, classical q-deformed kinetic equations, Kramers and Fokker-Planck equations, are also studied. Pacs: 05.20.Dd, 45.20.-d, 02.20.Uw Keywords: Kinetic theory, q-deformed classical mechanics, quantum groups, quantum algebras

cond-mat.stat-mech↗

arXiv2005

The Boltzmann temperature and Lagrange multiplier

We consider the relation between the Boltzmann temperature and the Lagrange multipliers associated with energy average in the nonextensive thermostatistics. In Tsallis' canonical ensemble, the Boltzmann temperature depends on energy through the probability distribution unless $q=1$. It is shown that the so-called 'physical temperature' introduced in [Phys. Lett. A \textbf{281} (2001) 126] is nothing but the ensemble average of the Boltzmann temperature.

cond-mat.stat-mech↗

arXiv2005

Canonical partition function for anomalous systems described by the $κ$-entropy

Starting from the $κ$-distribution function, obtained by applying the maximal entropy principle to the $κ$-entropy [G. Kaniadakis, Phys. Rev. E 66 (2002), 056125], we derive the expression of the canonical $κ$-partition function and discuss its main properties. It is shown that all important macroscopical quantities of the system can be expressed employing only the $κ$-partition function. The relationship between the associated $κ$-free energy and the $κ$-entropy is also discussed.

cond-mat.stat-mech↗

arXiv2005

Thermodynamic equilibrium and its stability for Microcanonical systems described by the Sharma-Taneja-Mittal entropy

It is generally assumed that the thermodynamic stability of equilibrium state is reflected by the concavity of entropy. We inquire, in the microcanonical picture, on the validity of this statement for systems described by the bi-parametric entropy $S_{_{κ, r}}$ of Sharma-Taneja-Mittal. We analyze the ``composability'' rule for two statistically independent systems, A and B, described by the entropy $S_{_{κ, r}}$ with the same set of the deformed parameters. It is shown that, in spite of the concavity of the entropy, the ``composability'' rule modifies the thermodynamic stability conditions of the equilibrium state. Depending on the values assumed by the deformed parameters, when the relation $S_{_{κ, r}}({\rm A}\cup{\rm B})> S_{_{κ, r}}({\rm A})+S_{_{κ, r}}({\rm B})$ holds (super-additive systems), the concavity conditions does imply the thermodynamics stability. Otherwise, when the relation $S_{_{κ, r}}({\rm A}\cup{\rm B})<S_{_{κ, r}}({\rm A})+S_{_{κ, r}}({\rm B})$ holds (sub-additive systems), the concavity conditions does not imply the thermodynamical stability of the equilibrium state.

cond-mat.stat-mech↗

arXiv2005

Canonical quantization of nonlinear many body systems

We study the quantization of a classical system of interacting particles obeying a recently proposed kinetic interaction principle (KIP) [G. Kaniadakis, Physica A {\bf 296}, 405 (2001)]. The KIP fixes the expression of the Fokker-Planck equation describing the kinetic evolution of the system and imposes the form of its entropy. In the framework of canonical quantization, we introduce a class of nonlinear Schrödinger equations (NSEs) with complex nonlinearities, describing, in the mean field approximation, a system of collectively interacting particles whose underlying kinetics is governed by the KIP. We derive the Ehrenfest relations and discuss the main constants of motion arising in this model. By means of a nonlinear gauge transformation of third kind it is shown that in the case of constant diffusion and linear drift the class of NSEs obeying the KIP is gauge-equivalent to another class of NSEs containing purely real nonlinearities depending only on the field $ρ=|ψ|^2$.

quant-ph↗

arXiv2005

q-deformed structures and generalized thermodynamics

On the basis of the recently proposed formalism [A. Lavagno and P.N. Swamy, Phys. Rev. E 65, 036101 (2002)], we show that the realization of the thermostatistics of q-deformed algebra can be built on the formalism of q-calculus. It is found that the entire structure of thermodynamics is preserved if we use an appropriate Jackson derivative instead of the ordinary thermodynamic derivative. Furthermore, in analogy with the quantum q-oscillator algebra, we also investigate a possible q-deformation of the classical Poisson bracket in order to extend a generalized q-deformed dynamics in the classical regime.

cond-mat.stat-mech↗

arXiv2005

Two-parameter deformations of logarithm, exponential, and entropy: A consistent framework for generalized statistical mechanics

A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging differential-functional equation yields a two-parameter class of generalized logarithms, from which entropies and power-law distributions follow: these distributions could be relevant in many anomalous systems. Within the specified range of parameters, these entropies possess positivity, continuity, symmetry, expansibility, decisivity, maximality, concavity, and are Lesche stable. The Boltzmann-Shannon entropy and some one parameter generalized entropies already known belong to this class. These entropies and their distribution functions are compared, and the corresponding deformed algebras are discussed.

cond-mat.stat-mech↗

arXiv2005

Canonical quantization of classical systems with generalized entropies

We present, in the framework of the canonical quantization, a class of nonlinear Schroedinger equations with a complex nonlinearity describing, in the mean field approximation, systems of collectively interacting particles. The quantum evolution equation is obtained starting from the study of a N-body classical system where the underlined nonlinear kinetics is governed by a kinetic interaction principle (KIP) recently proposed [G. Kaniadakis: Physica A 296 (2001), 405--425]. The KIP, both imposes the form of the generalized entropy associated to the classical system, and determines the Fokker-Planck equation describing the kinetic evolution of the system towards equilibrium. Keywords: Nonlinear Schroedinger equation, Nonlinear kinetics, Generalized entropy.

cond-mat.stat-mech↗

arXiv2005

A non self-referential expression of Tsallis' probability distribution function

The canonical probability distribution function (pdf) obtained by optimizing the Tsallis entropy under the linear mean energy constraint (first formalism) or the escort mean energy constraint (third formalism) suffer self-referentiality. In a recent paper [Phys. Lett. A {\bf335} (2005) 351-362] the authors have shown that the pdfs obtained in the two formalisms are equivalent to the pdf in non self-referential form. Based on this result we derive an alternative expression, which is non self-referential, for the Tsallis distributions in both first and third formalisms.

cond-mat.stat-mech↗

arXiv2004

Connections between Tsallis' formalisms employing the standard linear average energy and ones employing the normalized $q$-average energy

Tsallis' thermostatistics with the standard linear average energy is revisited by employing $S_{2-q}$, which is the Tsallis entropy with $q$ replaced by $2-q$. We explore the connections among the $S_{2-q}$ approach and the other different versions of Tsallis formalisms. It is shown that the normalized $q$-average energy and the standard linear average energy are related to each other. The relations among the Lagrange multipliers of the different versions are revealed. The relevant Legendre transform structures concerning the Lagrange multipliers associated with the normalization of probability are studied. It is shown that the generalized Massieu potential associated with $S_{2-q}$ and the linear average energy is related to one associated with the normalized Tsallis entropy and the normalized $q$-average energy.

cond-mat.stat-mech↗

arXiv2004

Generalized Kinetic Equations for a System of Interacting Atoms and Photons: Theory and Simulations

In the present paper we introduce generalized kinetic equations describing the dynamics of a system of interacting gas and photons obeying to a very general statistics. In the space homogeneous case we study the equilibrium state of the system and investigate its stability by means of Lyapounov's theory. Two physically relevant situations are discussed in details: photons in a background gas and atoms in a background radiation. After having dropped the statistics generalization for atoms but keeping the statistics generalization for photons, in the zero order Chapmann-Enskog approximation, we present two numerical simulations where the system, initially at equilibrium, is perturbed by an external isotropic Dirac's delta and by a constant source of photons.

cond-mat.stat-mech↗