We develop a statistical thermodynamic approach for understanding earthquake nucleation on homogeneous faults, explaining the occurrence of both self-arresting and run-away unstable ruptures (subshear and supershear events) previously observed in numerical simulations. Our theory identifies the conditions under which self-arresting earthquakes occur, based on critical sliding distance and dynamical stress drop. We also derive the Gutenberg-Richter distribution for these earthquakes, linking the fractal nature of faulting with the nucleation physics through the critical size's dependence on dynamical stress drop. Furthermore, we connect our findings to the dragon-king theory, which suggests that the largest earthquakes differ significantly in physical and statistical properties from smaller ones, offering new insights for earthquake prediction and risk assessment.