Topic

# Tsallis entropy

About: Tsallis entropy is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38122 citations.

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TL;DR: In this paper, a generalized form of entropy was proposed for the Boltzmann-Gibbs statistics with the q→1 limit, and the main properties associated with this entropy were established, particularly those corresponding to the microcanonical and canonical ensembles.

Abstract: With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS
q
≡k [1 – ∑
i=1
W
p
i
q
]/(q-1), whereq∈ℝ characterizes the generalization andp
i are the probabilities associated withW (microscopic) configurations (W∈ℕ). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as theq→1 limit.

8,239 citations

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TL;DR: The nonextensivity parameter q occurring in some of the applications of Tsallis statistics is shown to be given, in the q>1 case, entirely by the fluctuations of the parameters of the usual exponential distribution.

Abstract: The nonextensivity parameter $q$ occurring in some of the applications of Tsallis statistics (known also as index of the corresponding L\'evy distribution) is shown to be given, in the $qg1$ case, entirely by the fluctuations of the parameters of the usual exponential distribution.

620 citations

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TL;DR: In this article, it is shown that recourse to Tsallis' generalized entropy makes it possible to find sensible distribution functions for stellar polytropes, while that of Boltzmann yields unphysical distributions.

Abstract: It is shown that recourse to Tsallis' generalized entropy makes it possible to find sensible distribution functions for stellar polytropes, while that of Boltzmann yields unphysical distributions. Additionally, some constraints are imposed on Tsallis' entropy.

547 citations

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TL;DR: Tsallis entropy is applied as a general entropy formalism for information theory and for the first time image thresholding by nonextensive entropy is proposed regarding the presence of nonadditive information content in some image classes.

Abstract: Image analysis usually refers to processing of images with the goal of finding objects presented in the image. Image segmentation is one of the most critical tasks in automatic image analysis. The nonextensive entropy is a recent development in statistical mechanics and it is a new formalism in which a real quantity q was introduced as parameter for physical systems that present long range interactions, long time memories and fractal-type structures. In image processing, one of the most efficient techniques for image segmentation is entropy-based thresholding. This approach uses the Shannon entropy originated from the information theory considering the gray level image histogram as a probability distribution. In this paper, Tsallis entropy is applied as a general entropy formalism for information theory. For the first time image thresholding by nonextensive entropy is proposed regarding the presence of nonadditive information content in some image classes. Some typical results are presented to illustrate the influence of the parameter q in the thresholding.

490 citations

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TL;DR: In this paper, the authors construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics, which generalize the way in which ordinary Langevin equations underlie ordinary statistical mechanics to the more general nonextensive case.

Abstract: We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics. These systems generalize the way in which ordinary Langevin equations underlie ordinary statistical mechanics to the more general nonextensive case. As a main example, we construct a dynamical model of velocity fluctuations in a turbulent flow, which generates probability densities that very well fit experimentally measured probability densities in Eulerian and Lagrangian turbulence. Our approach provides a dynamical reason why many physical systems with fluctuations in temperature or energy dissipation rate are correctly described by Tsallis statistics.

447 citations