Exploring the Neighborhood of q-Exponentials

The q-exponential form [Formula: see text] is obtained by optimizing the nonadditive entropy [Formula: see text] (with [Formula: see text] , where BG stands for Boltzmann–Gibbs) under simple constraints, and emerges in wide classes of natural, artificial and social complex systems. However, in experiments, observations and numerical calculations, it rarely appears in its pure mathematical form. It appears instead exhibiting crossovers to, or mixed with, other similar forms. We first discuss departures from q-exponentials within crossover statistics, or by linearly combining them, or by linearly combining the corresponding q-entropies. Then, we discuss departures originated by double-index nonadditive entropies containing [Formula: see text] as particular case.