Overdamped Langevin dynamics

For potential $F$ and mobility $\mathcal{M}$, overdamped Langevin dynamics isThe matching noise amplitude is the fluctuation-dissipation relation that makes the Boltzmann density proportional to $e^{-F/(k_{B}T)}$ invariant.

For weak noise $D$ in a one-dimensional potential $\varphi$, escape from a minimum $m$ across a neighboring maximum $M$ occurs at leading rate