Connecting complex networks to nonadditive entropies

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.

Automated summary

The Boltzmann-Gibbs statistical mechanics is not always applicable to all systems, especially when dealing with complex systems involving nonlocal space-time entanglement. However, a generalization based on nonadditive q-entropies proves to be more effective in handling such systems. The study shows that scale-invariant networks fall into this category, indicating a connection between random geometric problems and thermal problems within the generalised thermostatistics. The q-generalisation of the Boltzmann-Gibbs exponential factor is a key aspect in understanding these systems, with the q=1 limit showing a recovery of the original factor.