Analysis of fractal groups of the type within the framework of Kaniadakis statistics

Souza, N. T. C. M.; Anselmo, D.H.A.L.; Mello, V.D.; Silva, R.

doi:10.1016/j.physleta.2014.04.030

Cited by 13 publications

(14 citation statements)

References 25 publications

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“…(24), we express j i , defined through Eqs. (9), (10) and (17), in terms of the functions a(•) and b(•) thus obtaining…”

Section: Lattice Expression Of the Fokker-planck Currentmentioning

confidence: 99%

“…Generalized statistical mechanics, based on κ-entropy [1,3,4], preserves the main features of ordinary Boltzmann-Gibbs statistical mechanics. For this reason, it has attracted the interest of many researchers over the last 16 years, who have studied its foundations and mathematical aspects [5][6][7][8][9][10][11][12], the underlying thermodynamics [13][14][15][16][17], and specific applications of the theory in various scientific and engineering fields. A non-exhaustive list of application areas includes quantum statistics [18][19][20], quantum entanglement [21,22], plasma physics [23][24][25][26][27], nuclear fission [28], astrophysics [29][30][31][32][33][34][35], geomechanics [36], genomics [37], complex networks [38,39], economy [40][41][42][43] and finance [44][45][46]…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Kinetics on a Lattice Featuring Anomalous Diffusion

Kaniadakis¹,

Hristopulos²

2018

Preprint

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Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker-Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker-Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker-Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker-Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP) that governs the particle kinetics of many body systems, introduced in [G. Kaniadakis, Physica A 296, 405 (2001)], univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker-Planck equation in its most general form.

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“…(24), we express j i , defined through Eqs. (9), (10) and (17), in terms of the functions a(•) and b(•) thus obtaining…”

Section: Lattice Expression Of the Fokker-planck Currentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear Kinetics on a Lattice Featuring Anomalous Diffusion

Kaniadakis¹,

Hristopulos²

2018

Preprint

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“…Therefore, the difference between the entropy of the system obtained from the composition of two statistically independent subsystems and the sum of the entropies of the two individual subsystems i.e. 13) results to be ∆S κ ≥ 0, and is given by A first remark that deserves attention regards the thermodynamic stability of system described by a generalized entropy. In the case of a system interacting with a bath in thermodynamic equilibrium, the particle density describing the state of the system in stationary conditions, is obtained starting from the maximum entropy principle.…”

Section: Let Us Introduce the κ-Parentropy Of A Normalized Set Of Promentioning

confidence: 99%

Composition law of κ -entropy for statistically independent systems

et al. 2017

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The intriguing and still open question concerning the composition law of κ-entropy S_{κ}(f)=1/2κ∑_{i}(f_{i}^{1-κ}-f_{i}^{1+κ}) with 0<κ<1 and ∑_{i}f_{i}=1 is here reconsidered and solved. It is shown that, for a statistical system described by the probability distribution f={f_{ij}}, made up of two statistically independent subsystems, described through the probability distributions p={p_{i}} and q={q_{j}}, respectively, with f_{ij}=p_{i}q_{j}, the joint entropy S_{κ}(pq) can be obtained starting from the S_{κ}(p) and S_{κ}(q) entropies, and additionally from the entropic functionals S_{κ}(p/e_{κ}) and S_{κ}(q/e_{κ}),e_{κ} being the κ-Napier number. The composition law of the κ-entropy is given in closed form and emerges as a one-parameter generalization of the ordinary additivity law of Boltzmann-Shannon entropy recovered in the κ→0 limit.

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“…Generalized statistical mechanics, based on the κ -exponential, preserves the main features of ordinary Boltzmann-Gibbs statistical mechanics which is based on the ordinary exponential through the Boltzmann factor. For this reason, it has attracted the interest of many researchers over the last two decades who have studied its foundations and mathematical aspects [49][50][51][52][53][54][55][56][57][58] , the underlying thermodynamics 59,60 , and specific applications of the theory to various fields. A non-exhaustive list of applications includes those in quantum statistics [61][62][63][64] , in quantum entanglement 65,66 , in plasma physics [67][68][69][70][71][72][73] , in nuclear fission [74][75][76][77] , in astrophysics [78][79][80][81] , in quantum gravity [82][83][84][85][86][87] , in geomechanics 88,89 , in genomics 90,91 , in complex networks [92]…”

mentioning

confidence: 99%

The κ-statistics approach to epidemiology

Kaniadakis

Baldi

Deisboeck

et al. 2020

Sci Rep

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A great variety of complex physical, natural and artificial systems are governed by statistical distributions, which often follow a standard exponential function in the bulk, while their tail obeys the Pareto power law. The recently introduced $$\kappa $$ κ -statistics framework predicts distribution functions with this feature. A growing number of applications in different fields of investigation are beginning to prove the relevance and effectiveness of $$\kappa $$ κ -statistics in fitting empirical data. In this paper, we use $$\kappa $$ κ -statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived $$\kappa $$ κ -Weibull distributions with data from the plague pandemic of 1417 in Florence as well as data from the COVID-19 pandemic in China over the entire cycle that concludes in April 16, 2020. As further validation of the proposed approach we present a more systematic analysis of COVID-19 data from countries such as Germany, Italy, Spain and United Kingdom, obtaining very good agreement between theoretical predictions and empirical observations. For these countries we also study the entire first cycle of the pandemic which extends until the end of July 2020. The fact that both the data of the Florence plague and those of the Covid-19 pandemic are successfully described by the same theoretical model, even though the two events are caused by different diseases and they are separated by more than 600 years, is evidence that the $$\kappa $$ κ -Weibull model has universal features.

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Analysis of fractal groups of the type within the framework of Kaniadakis statistics

Cited by 13 publications

References 25 publications

Nonlinear Kinetics on a Lattice Featuring Anomalous Diffusion

Nonlinear Kinetics on a Lattice Featuring Anomalous Diffusion

Composition law of κ -entropy for statistically independent systems

The κ-statistics approach to epidemiology

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