Publication: Multivariate group entropies, super-exponentially growing complex systems, and functional equations
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2020-12
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Amer Inst Physics
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Abstract
We define the class of multivariate group entropies as a novel set of information-theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality class of complex systems; in particular, we introduce a general entropy, representing a suitable information measure for this class. We also show that the group-theoretical structure associated with our multivariate entropies can be used to define a large family of exactly solvable discrete dynamical models. The natural mathematical framework allowing us to formulate this correspondence is offered by the theory of formal groups and rings.
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© 2020 Amer Inst Physics.
P.T. wishes to thank J. M. Amigo, M. A. Rodriguez, and G. Sicuro for useful discussions. This work has been partly supported by the research project PGC2018-094898-B-I00, Ministerio de Ciencia, Innovacion y Universidades, Spain, and by the Severo Ochoa Programme for Centres of Excellence in R&D"(CEX2019-000904-S), Ministerio de Ciencia, Innovacion y Universidades. P.T. is member of the Gruppo Nazionale di Fisica Matematica (INDAM), Italy.