Kaniadakis statistics and the quantum H-theorem

Santos, Adriana Paula Batista dos; Silva, R.; Alcaniz, J. S.; Anselmo, D.H.A.L.

doi:10.1016/j.physleta.2010.11.045

Cited by 20 publications

(25 citation statements)

References 38 publications

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“…Refs. [32,[36][37][38][39] for the non-Gaussian generalization of molecular chaos hypothesis). In particular, Maxwell expressions are recovered in the Gaussian limit, κ → 0.…”

Section: Discussionmentioning

confidence: 99%

Non-Gaussian statistics, Maxwellian derivation and stellar polytropes

Bento

Silva

2013

Physica A: Statistical Mechanics and its Applications

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In this letter we discuss two aspects of non-Gaussian statistics. In the first, we show that Maxwell's first derivation of the stationary distribution function for a dilute gas can be extended in the context of Kaniadakis statistics. In the second, by investigating the stellar system, we study the Kaniadakis analytical relation between the entropic parameter κ and the stellar polytrope index n. We compare also the Kaniadakis relation n = n(κ) with n = n(q) proposed in the Tsallis framework.

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“…Refs. [32,[36][37][38][39] for the non-Gaussian generalization of molecular chaos hypothesis). In particular, Maxwell expressions are recovered in the Gaussian limit, κ → 0.…”

Section: Discussionmentioning

confidence: 99%

Non-Gaussian statistics, Maxwellian derivation and stellar polytropes

Bento

Silva

2013

Physica A: Statistical Mechanics and its Applications

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“…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][93][94], in economy [95]…”

Section: A the κ-Deformed Exponential Functionmentioning

confidence: 99%

The κ-statistics approach to epidemiology

Kaniadakis

Baldi

Deisboeck

et al. 2020

Preprint

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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 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 κ-statistics in fitting empirical data. In this paper, we use κ-statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived 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 κ-Weibull model has universal features.

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“…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][47].…”

Section: Introductionmentioning

confidence: 99%

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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Kaniadakis statistics and the quantum H-theorem

Cited by 20 publications

References 38 publications

Non-Gaussian statistics, Maxwellian derivation and stellar polytropes

Non-Gaussian statistics, Maxwellian derivation and stellar polytropes

The κ-statistics approach to epidemiology

Nonlinear Kinetics on a Lattice Featuring Anomalous Diffusion

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