1. Connecting complex networks to nonadditive entropies.
- Author
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de Oliveira, R. M., Brito, Samuraí, da Silva, L. R., and Tsallis, Constantino
- Subjects
- *
BOLTZMANN-Gibbs distribution (Statistical physics) , *GEOMETRIC analysis , *STATISTICAL mechanics , *FUZZY measure theory , *SPECTRAL energy distribution - Abstract
Boltzmann–Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving nonlocal space–time entanglement. Its generalization based on nonadditive q-entropies adequately handles a wide class of such systems. We show here that scale-invariant networks belong to this class. We numerically study a d-dimensional geographically located network with weighted links and exhibit its 'energy' distribution per site at its quasi-stationary state. Our results strongly suggest a correspondence between the random geometric problem and a class of thermal problems within the generalised thermostatistics. The Boltzmann–Gibbs exponential factor is generically substituted by its q-generalisation, and is recovered in the q = 1 limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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