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

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  • Oikonomou, Th.

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.

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  • Oikonomou, Th., 2007. "Tsallis, Rényi and nonextensive Gaussian entropy derived from the respective multinomial coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 119-134.
  • Handle: RePEc:eee:phsmap:v:386:y:2007:i:1:p:119-134
    DOI: 10.1016/j.physa.2007.08.025
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    References listed on IDEAS

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    1. Suyari, Hiroki, 2006. "Mathematical structures derived from the q-multinomial coefficient in Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 63-82.
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    6. Borges, Ernesto P., 2004. "A possible deformed algebra and calculus inspired in nonextensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 95-101.
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    Cited by:

    1. Nelson, Kenric P. & Umarov, Sabir R. & Kon, Mark A., 2017. "On the average uncertainty for systems with nonlinear coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 30-43.
    2. Nelson, Kenric P. & Kon, Mark A. & Umarov, Sabir R., 2019. "Use of the geometric mean as a statistic for the scale of the coupled Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 248-257.
    3. Oikonomou, Thomas & Tirnakli, Ugur, 2009. "Generalized entropic structures and non-generality of Jaynes’ Formalism," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3027-3034.
    4. Oikonomou, Thomas, 2011. "Comment on “Critique of multinomial coefficient method for evaluating Tsallis and Rényi entropies” by A.S. Parvan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 781-784.

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