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Mathematical structures derived from the q-multinomial coefficient in Tsallis statistics

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  • Suyari, Hiroki

Abstract

We present q-Stirling's formula, q-multinomial coefficient, one-to-one correspondence between q-multinominal coefficient and Tsallis entropy, q-Pascal's triangle and a conjecture on the q-central limit theorem in Tsallis statistics for the generalization of the well-known fundamental formulas to systems exhibiting power-law behaviors. The main approach is based on the q-product, uniquely determined by Tsallis entropy, which has already been successfully applied to our recent proof of the law of error in Tsallis statistics.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:phsmap:v:368:y:2006:i:1:p:63-82
    DOI: 10.1016/j.physa.2005.12.061
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    References listed on IDEAS

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    6. Vignat, C & Hero III, A.O & Costa, J.A, 2004. "About closedness by convolution of the Tsallis maximizers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 147-152.
    7. T. Wada & A. M. Scarfone, 2005. "A non self-referential expression of Tsallis' probability distribution function," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 47(4), pages 557-561, October.
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    Cited by:

    1. Suyari, Hiroki & Wada, Tatsuaki, 2008. "Multiplicative duality, q-triplet and (μ,ν,q)-relation derived from the one-to-one correspondence between the (μ,ν)-multinomial coefficient and Tsallis entropy Sq," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 71-83.
    2. 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.
    3. Furuichi, Shigeru & Mitroi, Flavia-Corina, 2012. "Mathematical inequalities for some divergences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 388-400.
    4. 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.

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