A κ-entropic approach to the analysis of the fracture problem

Cravero, M.; Iabichino, G.; Kaniadakis, Giorgio; Miraldi, Elio; Scarfone, Antonio Maria

doi:10.1016/j.physa.2004.04.035

Cited by 24 publications

(15 citation statements)

References 23 publications

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“…An important physical example where the κ-distribution has been successfully applied is in the reproduction of the energy distribution of the fluxes of cosmic rays [30] (see also [51]). Moreover the κ-entropy has been applied in the study of the fracture propagation in brittle material, showing a good accordance with the results obtained experimentally and with the ones obtained through numerical simulations [52]. Finally, we recall that, like the previous one-parameter deformed entropic forms, also the κ-entropy fulfils many physically relevant proprieties.…”

Section: Kaniadakis Entropysupporting

confidence: 82%

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

Scarfone

Wada

2005

Phys. Rev. E

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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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Section: Kaniadakis Entropysupporting

confidence: 82%

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

Scarfone

Wada

2005

Phys. Rev. E

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“…Although the difference is not so large, this means that if an experimental data is well fitted with κ-exponential function it should not be well fitted with q-exponential one, and vice versa. Until now in the literature there are only a few experimental evidences which are well fitted with κ-exponential probability distributions: the flux distribution of the cosmic rays extends over 13 decades in energy [13]; the rain events in meteorology (the number density of rain events versus the event size) [13,14]; and the analysis of the fracture problem (the relation between the length of a transversal cut of the conducting thin ribbon and the electrical resistance) [15].…”

Section: Introductionmentioning

confidence: 99%

κ-generalization of Gauss' law of error

Wada

Suyari

2006

Physics Letters A

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Based on the κ-deformed functions (κ-exponential and κ-logarithm) and associated multiplication operation (κ-product) introduced by Kaniadakis (Phys. Rev. E 66 (2002) 056125), we present another one-parameter generalization of Gauss' law of error. The likelihood function in Gauss' law of error is generalized by means of the κ-product. This κ-generalized maximum likelihood principle leads to the so-called κ-Gaussian distributions.

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“…In the last few years, several applications of the κ-power law velocity distribution have been done in many disparate branches of physics [8][9][10][11][12][13][14][15][16][17][18][19][20][21]. However, such investigations are usually related with the κ-velocity distribution function as given by equation (6).…”

Section: Discussionmentioning

confidence: 99%

Conservative force fields in non-Gaussian statistics

Silva

Lima

2008

Physics Letters A

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In this letter, we determine the κ-distribution function for a gas in the presence of an external field of force described by a potential U(r). In the case of a dilute gas, we show that the κ-power law distribution including the potential energy factor term can rigorously be deduced in the framework of kinetic theory with basis on the Vlasov equation. Such a result is significant as a preliminary to the discussion on the role of long range interactions in the Kaniadakis thermostatistics and the underlying kinetic theory.

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A κ-entropic approach to the analysis of the fracture problem

Cited by 24 publications

References 23 publications

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

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

κ-generalization of Gauss' law of error

Conservative force fields in non-Gaussian statistics

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