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 [Formula: see text] limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas.
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| http://dx.doi.org/10.1038/s41598-020-80939-1 | DOI Listing |
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