From shape to randomness: A classification of Langevin stochasticity

► An “à la Mandelbrot” classification of randomness is established for Langevin dynamics. ► The classification applies to both stationary and transient Langevin dynamics. ► The classification has five states of randomness ranging from “infra-mild” to “ultra-wild”. ► We quantitatively describe how the dynamics' randomness is determined by the dynamics' potential. ► The classification results are highly applicable and highly implementable.