The Gutenberg-Richter law says earthquake frequency scales as a power law in magnitude: small earthquakes are exponentially more common than large ones, with a universal exponent. Power laws suggest criticality — the system poised at a phase transition where correlations extend to all scales. But criticality in what variable?
The fragment-asperity model provides an answer: surface energy. Earthquakes release elastic strain energy, and the release produces new fracture surface. The total surface energy scales with the earthquake's magnitude through the fragment size distribution. The paper shows that the Gutenberg-Richter power law is equivalent to thermodynamic criticality in the surface energy — the same mathematical structure as a system at its critical temperature.
The uniqueness of the surface-energy scaling is the key result. The model shows that surface energy is the only thermodynamic observable for which the fragment-asperity system exhibits critical behavior. Other observables — total energy, fragment number, strain release — do not show critical scaling. The Gutenberg-Richter law is not a generic signature of criticality but a specific signature of surface-energy criticality.
The implication: the seismogenic crust is critical in a precise sense. It's not that “everything is correlated” or “the system is complex” — it's that surface energy production is at its critical point, where fluctuations in fracture surface area diverge. The universal exponent of the Gutenberg-Richter law is a critical exponent, and the observable it applies to — surface energy — is uniquely singled out by the fragment-asperity dynamics.