Biomedical subjects

A M Scarfone

Publications and source records attributed to A M Scarfone.

4 recordsLinked to original sources

PubMed2005

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 states is reflected by the concavity of entropy. We inquire, in the microcanonical picture, about the validity of this statement for systems described by the two-parametric entropy S(kappa,r) of Sharma, Taneja, and Mittal. We analyze the "composability" rule for two statistically independent systems A and B, described by the entropy S(kappa,r) with the same set of the deformation 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 deformation parameters, when the relation S(kappa,r)(A union B) > S(kappa,r)(A) + S(kappa,r)(B) holds (superadditive systems), the concavity condition does imply thermodynamics stability. Otherwise, when the relation S(kappa,r)(A union B) < S(kappa,r)(A) + S(kappa,r)(B) holds (subadditive systems), the concavity condition does not imply thermodynamical stability of the equilibrium state.

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PubMed2005

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 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 the 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 rho=|psi|(2) .

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PubMed2005

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.

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PubMed2001

Quantum vortices in systems obeying a generalized exclusion principle.

The paper deals with a planar particle system obeying a generalized exclusion principle (EP) and governed, in the mean field approximation, by a nonlinear Schrödinger equation. We show that the EP involves a mathematically simple and physically transparent mechanism, which allows the genesis of quantum vortices in the system. We obtain in a closed form the shape of the vortices and investigate its main physical properties.

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