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Fractal geometry, information growth and nonextensive thermodynamics

Author

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

Abstract

This is a study of the information evolution of complex systems by a geometrical consideration. We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the information growth through the scale refinement. Due to the incompleteness of the state number counting at any scale on fractal support, the incomplete normalization ∑ipiq=1 is applied throughout the paper, where q is the fractal dimension divided by the dimension of the smooth Euclidean space in which the fractal structure of the phase space is embedded. It is shown that the information growth is nonadditive and is proportional to the trace-form ∑ipi−∑ipiq which can be connected to several nonadditive entropies. This information growth can be extremized to give power-law distributions for these nonequilibrium systems. It can also be used for the study of the thermodynamics derived from Tsallis entropy for nonadditive systems which contain subsystems each having its own q. It is argued that, within this thermodynamics, the Stefan–Boltzmann law of blackbody radiation can be preserved.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:340:y:2004:i:1:p:117-125
    DOI: 10.1016/j.physa.2004.03.086
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    Citations

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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. 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.

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