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Gibbs’ theorem for open systems with incomplete statistics

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  • Bağcı, G.B.

Abstract

Gibbs’ theorem, which is originally intended for canonical ensembles with complete statistics has been generalized to open systems with incomplete statistics. As a result of this generalization, it is shown that the stationary equilibrium distribution of inverse power law form associated with the incomplete statistics has maximum entropy even for open systems with energy or matter influx. The renormalized entropy definition given in this paper can also serve as a measure of self-organization in open systems described by incomplete statistics.

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  • Bağcı, G.B., 2009. "Gibbs’ theorem for open systems with incomplete statistics," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 265-269.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:265-269
    DOI: 10.1016/j.chaos.2008.11.018
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    References listed on IDEAS

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    1. Engel-Herbert, H. & Ebeling, W., 1988. "The behaviour of the entropy during transitions far from thermodynamic equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 149(1), pages 182-194.
    2. 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.
    3. 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.
    4. Abe, Sumiyoshi & Rajagopal, A.K, 2001. "Reexamination of Gibbs’ theorem and nonuniqueness of canonical ensemble theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 172-176.
    5. Engel-Herbert, H. & Ebeling, W., 1988. "The behaviour of the entropy during transitions far from thermodynamic equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 149(1), pages 195-205.
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    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.

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