Multivariate Group Entropies, Super-exponentially Growing Complex Systems and Functional Equations

Abstract

We define the class of multivariate group entropies, first investigated in [22], as a natural generalization of the Z-entropies introduced in [32]. We propose new examples related to the "super-exponential'" universality class of complex systems; in particular, we introduce a general entropy, suitable 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.