Rate-independent dynamics and Kramers-type phase transitions in nonlocal Fokker-Planck equations with dynamical control
نویسندگان
چکیده
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 timedependent constraint. In this paper we consider the fast reaction regime related to Kramers-type phase transitions and prove that the dynamics in the small-parameter limit can be described by a rate-independent evolution equation. To this end we derive mass-dissipation estimates from Muckenhoupt constants, establish dynamical peak-stability estimates, and employ moment estimates that encode large deviations results.
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