Identifying equilibration pathways beyond the α -relaxation: distinguishing the slow Arrhenius process from the...

Equilibration in liquids and glasses can proceed through multiple pathways, mediated by relaxation processes that remain active even when structural $\alpha$ -relaxation is strongly suppressed. Two prominent candidates are the Johari-Goldstein (JG) relaxation and the recently discovered slow Arrhenius process (SAP), both of which persist in the glassy state and exhibit a weaker temperature dependence than the structural relaxation. Their coexistence raises a central challenge: how to identify which localized process governs a given nonequilibrium kinetics. Here we compare the microscopic signatures of these two mechanisms and discuss practical strategies for their attribution. In particular, we argue that activation-energy matching provides only a first empirical indication, whereas SAP-driven kinetics can be identified more stringently within the collective small displacement (CSD) framework. The JG-controlled kinetics, on the contrary, should be assessed through consistency criteria tied to thermodynamic state of the system and $\alpha$ -dynamics. We believe that establishing such discriminating frameworks will be crucial for the next generation of experiments, simulations, and theoretical descriptions of nonequilibrium glassy dynamics.