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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.

Suggested Citation

  • 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. Th. Oikonomou & A. Provata, 2006. "Non-extensive trends in the size distribution of coding and non-coding DNA sequences in the human genome," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 259-264, March.
    2. 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.
    3. Sisto, R.P.Di & Martı́nez, S. & Orellana, R.B. & Plastino, A.R. & Plastino, A., 1999. "General thermostatistical formalisms, invariance under uniform spectrum translations, and Tsallis q-additivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(3), pages 590-613.
    4. Oikonomou, Th., 2007. "Properties of the “non-extensive Gaussian” entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 155-163.
    5. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
    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.
    7. Lenzi, E.K. & Mendes, R.S. & da Silva, L.R., 2000. "Statistical mechanics based on Renyi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 337-345.
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    Cited by:

    1. 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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