Abstract

Earthquakes, capable of causing widespread devastation, are complex multiscale phenomena. The Gutenberg-Richter law describes the power-law relationship between earthquake frequency and magnitude, while fault roughness, also exhibiting power-law behavior, influences rupture processes. The Rikitake time, an empirical relationship linking earthquake magnitude to the time required for stress accumulation, is affected by these multiscale characteristics. However, the underlying physics of this relationship remains poorly understood. This study demonstrates that the Rikitake time can be derived from the principles of multiscale thermodynamics, where energy dissipation at various scales governs system evolution. This supports the notion that faults evolve into smoother interfaces, capable of storing more stress prior to large earthquakes due to friction increase. Moreover, it also shows that multiscale thermodynamics can accurately describe different friction laws that are commonly employed in seismic modeling. It is also found a scaling between precursor and coseismic activity. This research provides a general friction law that incorporates multiscale thermodynamic principles, offering a deeper understanding of earthquake dynamics.