Exploring the Neighborhood of q-Exponentials |
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Authors: | Henrique Santos Lima Constantino Tsallis |
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Institution: | 1.Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, Rio de Janeiro, RJ 22290-180, Brazil;2.National Institute of Science and Technology of Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro, RJ 22290-180, Brazil;3.Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA;4.Complexity Science Hub Vienna, Josefstädter Strasse 39, 1080 Vienna, Austria |
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Abstract: | The q-exponential form is obtained by optimizing the nonadditive entropy (with , 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 as particular case. |
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Keywords: | q-exponentials nonextensive statistical mechanics nonadditive entropies complex systems |
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