Statistics of Binary Exchange of Energy or Money

Bertotti, Maria Letizia; Modanese, Giovanni

doi:10.3390/e19090465

Cited by 3 publications

(2 citation statements)

References 20 publications

(30 reference statements)

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“…Using the forward spatial derivative defined in (13), the function F n i can be shown to depend on the values of a(•), b(•), U(•) at the sites labeled by i, i + 1, i + 2. In contrast, the time difference of the discretized master equation (43) depends on the lattices sites i and i ± 1.…”

Section: A Temporal Discretizationmentioning

confidence: 99%

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Nonlinear Kinetics on Lattices Based on the Kinetic Interaction Principle

Kaniadakis

Hristopulos

2018

Entropy

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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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Section: A Temporal Discretizationmentioning

confidence: 99%

“…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 Lattices Based on the Kinetic Interaction Principle

Kaniadakis

Hristopulos

2018

Entropy

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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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Information Geometry of κ-Exponential Families: Dually-Flat, Hessian and Legendre Structures

Scarfone

Matsuzoe

Wada

2018

Entropy

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Abstract:In this paper, we present a review of recent developments on the κ-deformed statistical mechanics in the framework of the information geometry. Three different geometric structures are introduced in the κ-formalism which are obtained starting from three, not equivalent, divergence functions, corresponding to the κ-deformed version of Kullback-Leibler, "Kerridge" and Brègman divergences. The first statistical manifold derived from the κ-Kullback-Leibler divergence form an invariant geometry with a positive curvature that vanishes in the κ → 0 limit. The other two statistical manifolds are related to each other by means of a scaling transform and are both dually-flat. They have a dualistic Hessian structure endowed by a deformed Fisher metric and an affine connection that are consistent with a statistical scalar product based on the κ-escort expectation. These flat geometries admit dual potentials corresponding to the thermodynamic Massieu and entropy functions that induce a Legendre structure of κ-thermodynamics in the picture of the information geometry.

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Statistics of Binary Exchange of Energy or Money

Cited by 3 publications

References 20 publications

Nonlinear Kinetics on Lattices Based on the Kinetic Interaction Principle

Nonlinear Kinetics on Lattices Based on the Kinetic Interaction Principle

The κ-statistics approach to epidemiology

Information Geometry of κ-Exponential Families: Dually-Flat, Hessian and Legendre Structures

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