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Towards an information geometric characterization/classification of complex systems. I. Use of generalized entropies

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  • Ghikas, Demetris P.K.
  • Oikonomou, Fotios D.

Abstract

Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is to construct first some fundamental geometric objects which will be used in the development of our geometrical framework. We first establish the existence of a two-parameter family of probability distributions. Then using this family we derive the associated metric and we state a generalized Cramer–Rao Inequality. This gives a first two-parameter classification of complex systems. Finally computing the scalar curvature of the information manifold we obtain a further discrimination of the corresponding classes. Our analysis is based on the two-parameter family of generalized entropies of Hanel and Thurner (2011).

Suggested Citation

  • Ghikas, Demetris P.K. & Oikonomou, Fotios D., 2018. "Towards an information geometric characterization/classification of complex systems. I. Use of generalized entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 384-398.
    • Handle: RePEc:eee:phsmap:v:496:y:2018:i:c:p:384-398
    DOI: 10.1016/j.physa.2017.12.069
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    Cited by:

    1. López-Picón, J.L. & López-Vega, J. Manuel, 2021. "Information geometry for the strongly degenerate ideal Bose–Einstein fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).

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