Universal activated aging and weak ergodicity breaking in spin and structural glasses

Glasses possess complex energy landscapes and exhibit non-equilibrium aging dynamics. Here, we propose a generalized trap model for activated aging based on a key static property of the energy landscape: the distribution of energy barriers. Our theory predicts that, upon cooling, weak ergodicity breaking (WEB) in quenching dynamics occurs prior to strong ergodicity breaking in equilibrium dynamics. Furthermore, the theory indicates that the characteristic size of activation clusters can be deduced from the logarithmic decay of the time-correlation function. We rigorously test the model's assumptions and predictions using the simplest spin glass model - the random energy model. The predicted aging behavior is also universally observed in paradigmatic structural glasses, including the Weeks-Chandler-Andersen (WCA) model and amorphous silica. Remarkably, applying our framework to the WCA model allows us to extract a static length from the non equilibrium dynamics, extending its observable growth range from a mere factor of 2-3 to a full order of magnitude and providing supportive evidence for the random first-order transition scenario. Finally, we propose a unified ergodic-WEB phase diagram for aging dynamics in general glassy systems.