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An entropy based measure for comparing distributions of complexity

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  • Rajaram, R.
  • Castellani, B.

Abstract

This paper is part of a series addressing the empirical/statistical distribution of the diversity of complexity within and amongst complex systems. Here, we consider the problem of measuring the diversity of complexity in a system, given its ordered range of complexity types i and their probability of occurrence pi, with the understanding that larger values of i mean a higher degree of complexity. To address this problem, we introduce a new complexity measure called case-based entropyCc — a modification of the Shannon–Wiener entropy measure H. The utility of this measure is that, unlike current complexity measures–which focus on the macroscopic complexity of a single system–Cc can be used to empirically identify and measure the distribution of the diversity of complexity within and across multiple natural and human-made systems, as well as the diversity contribution of complexity of any part of a system, relative to the total range of ordered complexity types.

Suggested Citation

  • Rajaram, R. & Castellani, B., 2016. "An entropy based measure for comparing distributions of complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 35-43.
    • Handle: RePEc:eee:phsmap:v:453:y:2016:i:c:p:35-43
    DOI: 10.1016/j.physa.2016.02.007
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    References listed on IDEAS

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    1. Yamano, Takuya, 2004. "A statistical measure of complexity with nonextensive entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 131-137.
    2. Sean B. Carroll, 2001. "Chance and necessity: the evolution of morphological complexity and diversity," Nature, Nature, vol. 409(6823), pages 1102-1109, February.
    3. Rojdestvenski, I. & Cottam, M.G. & Oquist, G. & Huner, N., 2003. "Thermodynamics of complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 318-328.
    4. Contreras-Reyes, Javier E., 2015. "Rényi entropy and complexity measure for skew-gaussian distributions and related families," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 84-91.
    5. Geoffrey B. West & James H. Brown & Brian J. Enquist, 1997. "A General Model for the Origin of Allometric Scaling Laws in Biology," Working Papers 97-03-019, Santa Fe Institute.
    6. Brian Castellani & Rajeev Rajaram, 2012. "Case-based modeling and the SACS Toolkit: a mathematical outline," Computational and Mathematical Organization Theory, Springer, vol. 18(2), pages 153-174, June.
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    Cited by:

    1. Geng, Zhiqiang & Li, Yanan & Han, Yongming & Zhu, Qunxiong, 2018. "A novel self-organizing cosine similarity learning network: An application to production prediction of petrochemical systems," Energy, Elsevier, vol. 142(C), pages 400-410.
    2. R. Rajaram & B. Castellani & A. N. Wilson, 2017. "Advancing Shannon Entropy for Measuring Diversity in Systems," Complexity, Hindawi, vol. 2017, pages 1-10, May.

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