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Related papers: On cumulative Tsallis entropies

200 papers

The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are…

Classical Physics · Physics 2016-11-15 B. H. Lavenda , J. Dunning-Davies

In this paper, we investigate new procedures for statistical testing based on Tsallis entropy, a parametric generalization of Shannon entropy. Focusing on multivariate generalized Gaussian and $q$-Gaussian distributions, we develop…

Methodology · Statistics 2025-06-18 Mehmet Sıddık Çadırcı

A formal correspondence between the q-distribution obtained from the Tsallis entropy and non-maxwellian distributions obtained from the Boltzmann-Gibbs entropy is afforded.

Quantum Physics · Physics 2009-11-13 N. G. de Almeida

In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp…

Risk Management · Quantitative Finance 2025-11-24 Baishuai Zuo , Chuancun Yin

We present a path toward determining the statistical origin of the thermodynamic limit for systems with long-range interactions. We assume throughout that the systems under consideration have thermodynamic properties given by the Tsallis…

Statistical Mechanics · Physics 2015-06-18 Nikos Kalogeropoulos

Nonadditive Tsallis $q$-statistics has successfully been applied for a plethora of systems in natural sciences and other branches of knowledge. Nevertheless, its foundations have been severely criticised by some authors based on the…

Statistical Mechanics · Physics 2020-05-20 J. A. S. Lima , A. Deppman

We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…

Data Analysis, Statistics and Probability · Physics 2007-10-24 Peter Sunehag

We study the estimation of Tsallis entropy of a finite number of independent populations, each following an exponential distribution with the same scale parameter and distinct location parameters for $q>0$. We derive a Stein-type improved…

Statistics Theory · Mathematics 2024-01-18 Naveen Kumar , Ambesh Dixit , Vivek Vijay

We first observe that the (co)domains of the q-deformed functions are some subsets of the (co)domains of their ordinary counterparts, thereby deeming the deformed functions to be incomplete. In order to obtain a complete definition of…

Statistical Mechanics · Physics 2015-05-13 Thomas Oikonomou , G. Baris Bagci

In this letter, we study the limit behavior of the evolution of Tsallis entropy in self-gravitating systems. The study is carried out under two different situations, drawing the same conclusion. No matter in the energy transfer process or…

Statistical Mechanics · Physics 2017-10-11 Yahui Zheng , Jiulin Du , Faku Liang

We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…

Statistical Mechanics · Physics 2009-10-31 R. Salazar , R. Toral

This is an analysis of the additivity of the entropy of thermodynamical systems with finite heat baths. It is presented an expression for the physical entropy of weakly interacting ergodic systems, and it is shown that it is valid for both…

Statistical Mechanics · Physics 2007-05-23 M. P. Almeida

Numerical experiments support the interesting conjecture that statistical methods be applicable not only to fully-chaotic systems, but also at the edge of chaos by using Tsallis' generalizations of the standard exponential and entropy. In…

Statistical Mechanics · Physics 2017-08-23 Marcello Lissia , Massimo Coraddu , Roberto Tonelli

We revisit the issues on the thermodynamic property of stellar self-gravitating system arising from Tsallis' non-extensive entropy. Previous papers (Taruya & Sakagami, Physica A 307 (2002) 185 (cond-mat/0107494); ibid. (2002) in press…

Statistical Mechanics · Physics 2009-11-07 Atsushi Taruya , Masa-aki Sakagami

Generalizing the group structure of the Euclidean space, we construct a Riemannian metric on the deformed set \ $\mathbb{R}^n_q$ \ induced by the Tsallis entropy composition property. We show that the Tsallis entropy is a "hyperbolic…

Mathematical Physics · Physics 2015-06-03 Nikos Kalogeropoulos

We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $\Lambda$ as inverses of these distribution functions, we are led to a…

Statistical Mechanics · Physics 2007-05-23 Rudolf Hanel , Stefan Thurner

In this paper, we consider the problem of estimating Tsallis entropy from a given data set. We propose four different estimators for Tsallis entropy measure based on higher-order sample spacings, and then discuss estimation of Tsallis…

Methodology · Statistics 2026-02-10 Siddhartha Chakraborty , Asok K. Nanda , Narayanaswamy Balakrishnan

There is a conception that Boltzmann-Gibbs statistics cannot yield the long tail distribution. This is the justification for the intensive research of nonextensive entropies (i.e. Tsallis entropy and others). Here the error that caused this…

Information Theory · Computer Science 2009-06-30 Oded Kafri

An axiomatic foundation regarding the entropy for complex systems is established. Missing from decades of research was the requirement that entropy must measure the uncertainty at the informational scale of the maximizing distribution,…

Statistical Mechanics · Physics 2026-05-29 Kenric P. Nelson

The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they…

Statistical Mechanics · Physics 2009-11-07 Sumiyoshi Abe