Quantum entanglement and Kaniadakis entropy

Ourabah, Kamel; Hamici-Bendimerad, Amel Hiba; Tribeche, Mouloud

doi:10.1088/0031-8949/90/4/045101

Cited by 39 publications

(26 citation statements)

References 44 publications

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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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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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“…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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“…Quantum entropic measures are of use in diverse areas of active research. For example, they find applications as uncertainty measures (as is the case in the study of uncertainty relations [15][16][17][18][19][20]); in entanglement measuring and detection [21][22][23][24][25][26][27]; as measures of mutual information [28][29][30][31]; and they are of great importance in the theory of quantum coding and quantum information transmission [1,2,[32][33][34].…”

Section: Introductionmentioning

confidence: 99%

A family of generalized quantum entropies: definition and properties

Bosyk

Zozor

Holik

et al. 2016

Quantum Inf Process

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We present a quantum version of the generalized $(h,\phi)$-entropies, introduced by Salicr\'u \textit{et al.} for the study of classical probability distributions. We establish their basic properties, and show that already known quantum entropies such as von Neumann, and quantum versions of R\'enyi, Tsallis, and unified entropies, constitute particular classes of the present general quantum Salicr\'u form. We exhibit that majorization plays a key role in explaining most of their common features. We give a characterization of the quantum $(h,\phi)$-entropies under the action of quantum operations, and study their properties for composite systems. We apply these generalized entropies to the problem of detection of quantum entanglement, and introduce a discussion on possible generalized conditional entropies as well.Comment: 26 pages, 1 figure. Close to published versio

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Quantum entanglement and Kaniadakis entropy

Cited by 39 publications

References 44 publications

The κ-statistics approach to epidemiology

The κ-statistics approach to epidemiology

Nonlinear Kinetics on a Lattice Featuring Anomalous Diffusion

A family of generalized quantum entropies: definition and properties

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