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A new expression of the probability distribution in Incomplete Statistics and fundamental thermodynamic relations

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  • Huang, Zhifu
  • Lin, Bihong
  • Chen, Jincan

Abstract

In order to overcome the limitations of the original expression of the probability distribution appearing in literature of Incomplete Statistics, a new expression of the probability distribution is derived, where the Lagrange multiplier β introduced here is proved to be identical with that introduced in the second and third choices for the internal energy constraint in Tsallis’ statistics and to be just equal to the physical inverse temperature. It is expounded that the probability distribution described by the new expression is invariant through uniform translation of the energy spectrum. Moreover, several fundamental thermodynamic relations are given and the relationship between the new and the original expressions of the probability distribution is discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1277-1281
    DOI: 10.1016/j.chaos.2007.09.002
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    References listed on IDEAS

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    1. Wang, Q.A. & Nivanen, L. & Le Méhauté, A. & Pezeril, M., 2004. "Fractal geometry, information growth and nonextensive thermodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 117-125.
    2. Ou, Congjie & Chen, Jincan, 2006. "Two long-standing problems in Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 525-529.
    3. 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.
    4. Ou, Congjie & Chen, Jincan & Wang, Qiuping A., 2006. "Temperature definition and fundamental thermodynamic relations in incomplete statistics," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 518-521.
    5. 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.
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    Cited by:

    1. 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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