A Network-Based Energy Transport Model for Earthquakes and Aftershocks

We investigate the dynamics of earthquakes and aftershocks through a network-based model of energy transport. In this framework, discrete energy quanta perform random walks on the nodes of a complex network, representing stress redistribution within a fault system. Motivated by empirical seismic observations, we incorporate two key ingredients: energy dissipation, accounting for stress loss during slip events, and stress readjustments, mimicking post-event redistribution. Unlike traditional models, our approach does not rely on triggering kernels, stress transfer rules, or critical state assumptions. Within this minimal yet physically grounded setup, synthetic earthquake time series exhibit aftershock sequences and statistical correlations that emerge naturally from internal fluctuations. We define earthquake magnitude as the deviation of the number of energy quanta from its mean, providing a simple proxy for stress release. Remarkably, this mechanism reproduces three fundamental empirical laws of seismology : Omori's law, the Gutenberg–Richter law, and Bath's law with excellent quantitative agreement. Our results demonstrate that essential features of seismicity can emerge from basic principles of energy transport and dissipation on complex networks.