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Multiscale Complexity/Entropy

Author

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  • Y. BAR-YAM

    (New England Complex Systems Institute, 24 Mt. Auburn St., Cambridge, MA, 02138, USA)

Abstract

We discuss the role of scale dependence of entropy/complexity and its relationship to component interdependence. The complexity as a function of scale of observation is expressed in terms of subsystem entropies for a system having a description in terms of variables that have the samea prioriscale. The sum of the complexity over all scales is the same for any system with the same number of underlying degrees of freedom (variables), even though the complexity at specific scales differs due to the organization/interdependence of these degrees of freedom. This reflects a tradeoff of complexity at different scales of observation. Calculation of this complexity for a simple frustrated system reveals that it is possible for the complexity to be negative. This is consistent with the possibility that observations of a system that include some errors may actually cause, on average, negative knowledge, i.e. incorrect expectations.

Suggested Citation

  • Y. Bar-Yam, 2004. "Multiscale Complexity/Entropy," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 47-63.
    • Handle: RePEc:wsi:acsxxx:v:07:y:2004:i:01:n:s0219525904000068
    DOI: 10.1142/S0219525904000068
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    Cited by:

    1. Răzvan-Cornel Sfetcu & Vasile Preda, 2023. "Fractal Divergences of Generalized Jacobi Polynomials," Mathematics, MDPI, vol. 11(16), pages 1-12, August.
    2. Chen, Yanguang & Feng, Jian, 2017. "Spatial analysis of cities using Renyi entropy and fractal parameters," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 279-287.
    3. Chen, Yanguang, 2020. "Equivalent relation between normalized spatial entropy and fractal dimension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).

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