Phase transitions in a nonlocal Fokker-Planck equation with multiple time scales

Many-particle storage systems can be modelled by a nonlocal Fokker-Planck equation that describes energy minimisation in a double well-potential, involves two small parameters and is driven by a time-dependent constraint. The dynamics takes place on three different time scales and can produce several types of hysteretic or non-hysterectic phase transitions. Formal asymptotic analysis allows to derive reduced dynamical models for different small-parameter limits. In this talk we in particular discuss the fast-reaction regime that is governed by Kramer's formula, and also indicate how the limit procedure can be made rigorous

This is joint work with Michael Herrmann and Juan Velazquez.