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=1q=1 limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas.

R. de Oliveira, S. Brito, L. da Silva, C. Tsallis, Connecting complex networks to nonadditive entropies, Scientific Reports 11 (2021) 1130