Nonextensive foundation of Lévy distributions

Prato, Domingo; Tsallis, Constantino

doi:10.1103/physreve.60.2398

Cited by 175 publications

(149 citation statements)

References 21 publications

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“…Although, the PDFs have been studied before in Ref. 31,32 we show the PDFs and fits to the analytically found PDFs for completeness and for reference during the q-entropy study. Thus, we will now focus on solving Eq.…”

Section: Numerical Solutions To the Fractional Fokker-planck Equmentioning

confidence: 99%

A fractional Fokker-Planck model for anomalous diffusion

2014

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In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality of the stable Lévy distribution.The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.

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Section: Numerical Solutions To the Fractional Fokker-planck Equmentioning

confidence: 99%

A fractional Fokker-Planck model for anomalous diffusion

2014

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“…For example, x may be associated with a single jump length of a free Brownian particle [10,39] so that p(x) stands for a single jump length distribution. Optimizing S[p(x)] with additional constraints imposed on p(x)…”

Section: Lévy Noises and Tsallis Thermodynamicsmentioning

confidence: 99%

Resonant activation in the presence of nonequilibrated baths

Dybiec

Gudowska–Nowak

2004

Phys. Rev. E

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We study the generic problem of the escape of a classical particle over a fluctuating barrier under the influence of non-Gaussian noise mimicking the effects of not-fully equilibrated bath. Our attention focuses on the effect of the stable noises on the mean escape time and on the phenomenon of resonant activation (RA). Possible physical interpretation of the occurrence of Lévy noises in the system of interest is discussed and the connection between the Tsallis statistics and the Fractional Fokker Planck Equation is addressed.PACS numbers: 05.10.-a, 05.90+m, 02.50.-r, 82.20.-w

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“…Tsallis showed [9,10] that such probability distributions correspond with Lévy α-stable distributions (α ∈ 0, 2 ) where…”

Section: Introductionmentioning

confidence: 99%

Non-Extensive Statistical Mechanics - a Possible Basis for Modelling Processes in Computer Memory System

Strzałka

2010

Acta Phys. Pol. A

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Tsallis definition of non-extensive entropy introduced in 1988 has been considered to obtain new possibilities to construct generalized thermodynamical basis for statistical physics expanding classical Boltzmann-Gibbs thermodynamics for nonequilibrium states. During the last two decades this q-generalized theory has been successfully applied to considerable number of physically interesting complex phenomena. In the paper the possible thermodynamical basis of processes will be presented in nowadays computer systems in the case of memory behaviour.

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Nonextensive foundation of Lévy distributions

Cited by 175 publications

References 21 publications

A fractional Fokker-Planck model for anomalous diffusion

A fractional Fokker-Planck model for anomalous diffusion

Resonant activation in the presence of nonequilibrated baths

Non-Extensive Statistical Mechanics - a Possible Basis for Modelling Processes in Computer Memory System

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