When may a system be referred to as complex?—an entropic perspective - Tsallis, Constantino (Frontiers in Complex Systems, 2023)
Defining complexity is hard and far from unique -like defining beauty, intelligence, creativity, and many other such abstracts concepts. In contrast, describing concrete complex systems is a sensibly simpler task. We focus here on such issue from the perspective of entropic functionals, either additive or nonadditive. Indeed, for the systems currently referred to as simple, the statistical mechanics and associated (additive) entropy certainly is that of Boltzmann-Gibbs, formulated 150 years ago. This formalism constitutes a pillar of contemporary theoretical physics, and is typically grounded on strong chaos, mixing, ergodicity, and similar hypothesis which typically emerge for systems with short-range space-time generic correlations. It fails, however, for the so-called complex systems, where generic long-range space-time correlations prevail, typically grounded on weak chaos. Many such nontrivial systems are satisfactorily handled within a generalization of the Boltzmann-Gibbs theory, namely nonextensive statistical mechanics, introduced in 1988, and grounded on nonadditive entropies. Illustrations are presented in terms of D-dimensional simplexes such as nodes (D = 0), bonds (D = 1), plaquettes (D = 2), polyhedra (D = 3, . . . ), and higher-order ones. A regularly updated Bibliography is available at http://tsallis.cat. cbpf.br/biblio.htm