Tsallis, Rényi and nonextensive Gaussian entropy derived from the respective multinomial coefficients

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12 Citations (Scopus)

Abstract

We explore the generalization of the ordinary multinomial coefficient, based on the deformed q-multiplication and q-division. Aim of this study is to construct the appropriate multinomial coefficients, from which one can obtain the Tsallis, Rényi and nonextensive Gaussian entropy, respectively. We show that for all three above entropies there are two possible ways to define the generalized multinomial coefficient. Its consequence is discussed.

Original languageEnglish
Pages (from-to)119-134
Number of pages16
JournalPhysica A: Statistical Mechanics and its Applications
Volume386
Issue number1
DOIs
Publication statusPublished - Dec 1 2007
Externally publishedYes

Fingerprint

Multinomial Coefficients
Entropy
entropy
coefficients
multiplication
division
Division
Multiplication

Keywords

  • Generalized factorial
  • Generalized multinomial coefficient
  • Nonextensive Gaussian entropy
  • Rényi entropy
  • Tsallis entropy

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

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abstract = "We explore the generalization of the ordinary multinomial coefficient, based on the deformed q-multiplication and q-division. Aim of this study is to construct the appropriate multinomial coefficients, from which one can obtain the Tsallis, R{\'e}nyi and nonextensive Gaussian entropy, respectively. We show that for all three above entropies there are two possible ways to define the generalized multinomial coefficient. Its consequence is discussed.",
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AB - We explore the generalization of the ordinary multinomial coefficient, based on the deformed q-multiplication and q-division. Aim of this study is to construct the appropriate multinomial coefficients, from which one can obtain the Tsallis, Rényi and nonextensive Gaussian entropy, respectively. We show that for all three above entropies there are two possible ways to define the generalized multinomial coefficient. Its consequence is discussed.

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KW - Generalized multinomial coefficient

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KW - Rényi entropy

KW - Tsallis entropy

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