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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 requirements. In particular, we introduce an extensivity postulate as a natural requirement for an information measure to be meaningful. The information measures proposed are suitably defined for describing universality classes of complex systems, each characterized by a specific phase space growth rate function.
In the past three decades, many theoretical measures of complexity have been proposed to help understand complex systems. In this work, for the first time, we place these measures on a level playing field, to explore the qualitative similarities and
The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general composabilit
Motivated by experimental observations of patterning at the leading edge of motile eukaryotic cells, we introduce a general model for the dynamics of nearly-flat fluid membranes driven from within by an ensemble of activators. We include, in particul
In the usual statistical model of a dense polymer (a single space-filling loop on a lattice) in two dimensions the loop does not cross itself. We modify this by including intersections in which {em three} lines can cross at the same point, with some
We study the conditions under which the critical behavior of the three-dimensional $mn$-vector model does not belong to the spherically symmetrical universality class. In the calculations we rely on the field-theoretical renormalization group approac