Gamma function to Beck–Cohen superstatistics

Han, Jung Hun

doi:10.1016/j.physa.2013.05.041

Cited by 5 publications

(1 citation statement)

References 20 publications

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“…(see [2,3,11,18,24,25]). Equation (18) is the superstatistics of Beck and Cohen [3], in the sense of superimposing another distribution or the distribution of x with superimposed distribution of the parameter θ.…”

Section: Superstatistics Consideration and Pathway Modelmentioning

confidence: 99%

An Overview of the Pathway Idea and Its Applications in Statistical and Physical Sciences

Sebastian

Nair²,

Joseph³

2015

Axioms

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Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter α, called the pathway parameter, one can connect generalized type-1 beta family of densities, generalized type-2 beta family of densities, and generalized gamma family of densities, in the scalar as well as the matrix cases, also in the real and complex domains. It is shown that when the model is applied to physical situations then the current hot topics of Tsallis statistics and superstatistics in statistical mechanics become special cases of the pathway model, and the model is capable of capturing many stable situations as well as the unstable or chaotic neighborhoods of the stable situations and transitional stages. The pathway model is shown to be connected to generalized information measures or entropies, power law, likelihood ratio criterion or λ−criterion in multivariate statistical analysis, generalized Dirichlet densities, fractional calculus, Mittag-Leffler stochastic process, Krätzel integral in applied analysis, and many other topics in different disciplines. The pathway model enables one to extend the current results on quadratic and bilinear forms, when the samples come from Gaussian populations, to wider classes of populations.Axioms 2015, 4 531

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Section: Superstatistics Consideration and Pathway Modelmentioning

confidence: 99%

An Overview of the Pathway Idea and Its Applications in Statistical and Physical Sciences

Sebastian

Nair²,

Joseph³

2015

Axioms

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Mittag-Leffler functions in superstatistics

Santos

2020

Chaos, Solitons & Fractals

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Nowadays, there is a series of complexities in biophysics that require a suitable approach to determine the measurable quantity. In this way, the superstatistics has been an important tool to investigate dynamic aspects of particles, organisms and substances immersed in systems with non-homogeneous temperatures (or diffusivity). The superstatistics admits a general Boltzmann factor that depends on the distribution of intensive parameters β = 1 D (inverse-diffusivity). Each value of β is associated with a local equilibrium in the system. In this work, we investigate the consequences of Mittag-Leffler function on the definition of f (β)-distribution of a complex system. Thus, using the techniques belonging to the fractional calculus with non-singular kernels, we constructed a distribution to β using the Mittag-Leffler function. This function implies distributions with power-law behaviour to high energy values in the context of Cohen-Beck superstatistics. This work aims to present the generalised probabilities distribution in statistical mechanics under a new perspective of the Mittag-Leffler function inspired in Atangana-Baleanu and Prabhakar forms.

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