A model for diffusive systems: Beyond the Arrhenius mechanism

Diffusivity in supercooled liquids was observed to exhibit a non-Arrhenius behavior near the glass-transition temperature. This process, which occurs where the activation energy depends on the temperature, suggests the possibility of a metastable equilibrium. This peculiar phenomenon cannot be explained using the usual Markovian stochastic models. Based on a non-linear Fokker-Planck equation, we propose a diffusion coefficient that is proportional to the supercooled-liquid concentration. The proposed model allows us to explain the anomalous behavior of the diffusivity robustly. We demonstrate that this new approach is consistent with experimental patterns. Besides, it could be applied to non-Arrhenius chemical kinetics.