THERMODYNAMICS OF FRACTAL NETWORKS

Optimal channel networks are fractal structures that bear a striking r esemblance to real rivers. They are obtained by minimizing an energy f unctional associated with spanning trees. We show that large network d evelopment effectively occurs al zero temperature since the entropy sc ales subdominantly with system size compared to the energy. Thus these networks develop under generic conditions and freeze into a static sc ale-free structure. We suggest a link of optimal channel networks with self-organized critical systems and critical phenomena which exhibit spatial and temporal fractality, the former under generic conditions a nd the latter on fine tuning.