Route of Random Process to Ultraslow Aging Phenomena

Logarithmic aging phenomena are prevalent in various systems, including electronic materials and biological structures. This Letter utilizes a generalized continuous-time random walk framework to investigate the mechanisms behind the logarithmic aging phenomena. By incorporating non-Markovian processes with significant memory effects, we modify traditional diffusion models to exhibit logarithmic decay in both survival and returning probabilities. Importantly, we analyze the impact of aging on autocorrelation functions, illustrating how long-term memory behaviors affect the temporal evolution of physical observables. These results connect microscopic models to macroscopic manifestations in real-world systems, advancing the understanding of ultraslow dynamics in disordered systems.