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

Demetris P.K. Ghikas and Fotios D. Oikonomou

Physica A: Statistical Mechanics and its Applications, 2018, vol. 496, issue C, 384-398

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).

Keywords: Complex systems; Generalized entropies; Information geometry (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:496:y:2018:i:c:p:384-398

DOI: 10.1016/j.physa.2017.12.069

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