  The hysteretic behavior of many-particle systems with non-convex free energy
can be modeled by nonlocal Fokker-Planck equations that involve two small
parameters and are driven by a time- dependent constraint. In this paper we
consider the fast reaction regime related to Kramers-type phase transitions and
show that the dynamics in the small-parameter limit can be described by a
rate-independent evolution equation with hysteresis. For the proof we first
derive mass-dissipation estimates by means of Muckenhoupt constants, formulate
conditional stability estimates, and char- acterize the mass flux between the
different phases in terms of moment estimates that encode large deviation
results. Afterwards we combine all these partial results and establish the
dynamical sta- bility of localized peaks as well as sufficiently strong
compactness results for the basic macroscopic quantities.
