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Updated: Nov 25, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Exploring the Neighborhood of q-Exponentials
Henrique Santos Lima1, Constantino Tsallis1,2,3,4
1Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, Rio de Janeiro, RJ 22290-180, Brazil.
Abstract:
The q-exponential form eqx≡[1+(1-q)x]1/(1-q)(e1x=ex) is obtained by optimizing the nonadditive entropy Sq≡k1-∑ipiqq-1 (with S1=SBG≡-k∑ipilnpi, 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 Sq as particular case.
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