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Applying incomplete statistics to nonextensive systems with different q indices

Author

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  • Nivanen, L.
  • Pezeril, M.
  • Wang, Q.A.
  • Méhauté, A. Le

Abstract

The nonextensive statistics based on the q-entropy Sq=-∑i=1v(pi-piq)1-q has been so far applied to systems in which the q value is uniformly distributed. For the systems containing different q’s, the applicability of the theory is still a matter of investigation. The difficulty is that the class of systems to which the theory can be applied is actually limited by the usual nonadditivity rule of entropy which is no more valid when the systems contain non uniform distribution of q values. In this paper, within the framework of the so called incomplete information theory, we propose a more general nonadditivity rule of entropy prescribed by the zeroth law of thermodynamics. This new nonadditivity generalizes in a simple way the usual one and can be proved to lead uniquely to the q-entropy.

Suggested Citation

  • Nivanen, L. & Pezeril, M. & Wang, Q.A. & Méhauté, A. Le, 2005. "Applying incomplete statistics to nonextensive systems with different q indices," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1337-1342.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:5:p:1337-1342
    DOI: 10.1016/j.chaos.2004.09.064
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    Cited by:

    1. Huang, Zhifu & Lin, Bihong & Chen, Jincan, 2009. "A new expression of the probability distribution in Incomplete Statistics and fundamental thermodynamic relations," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1277-1281.
    2. Bağcı, G.B., 2009. "Gibbs’ theorem for open systems with incomplete statistics," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 265-269.

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