Abstract
We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series of natural axioms. In addition, we require extensivity in order to ensure that our information measures are meaningful. The entropic measures proposed are suitably defined for describing universality classes of complex systems, each characterized by a specific state space growth rate function.
Highlights
The aim of this paper is to propose a general theoretical construction that allows us to associate a given class of complex systems with a suitable information measure adapted to this class, and expressed by an entropic functional mathematically deduced from a set of axioms, belonging to the family of group entropies[1,2,3]
We propose to look for new information measures, written in terms of entropic functionals that are designed according to the specific properties of the system, or family of systems, under consideration
From a mathematical point of view, the derivation of each of these entropic measures is a direct consequence of an axiomatic approach, based on formal group theory
Summary
The aim of this paper is to propose a general theoretical construction that allows us to associate a given class of complex systems with a suitable information measure adapted to this class, and expressed by an entropic functional mathematically deduced from a set of axioms, belonging to the family of group entropies[1,2,3]. We propose to look for new information measures, written in terms of entropic functionals that are designed according to the specific properties of the system, or family of systems, under consideration To this aim, we shall prove a theorem that allows us to associate with a given universality class of systems a specific entropic measure, constructed in a completely algorithmic way. The deep insights represented by the Tononi-Edelman-Spons Integrated Information concept is traditionally formulated mathematically in terms of sums of conditioned entropies of partitions of the considered system, in particular the human brain.
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