Generalized Einstein relation for aging processes

This paper investigates physical aging processes using a minimal Langevin model. A generalized Einstein relation is proposed, extending its application to non-equilibrium situations where damping and temperature decrease with time. This relation is used to analyze anomalous diffusion, showing power-law diffusion away from the critical point and logarithmic Sinai-type ultra-slow diffusion at the critical point. The study explores weak ergodicity breaking and its connection to the generalized Einstein relation, concluding that irreversibility and convergence of time-averaged observables alone are insufficient for ergodicity. Applications to granular gases are also discussed.

Jing-Dong Bao, Xiang-Rong Wang