Stability reversal, activated escape, and mechanical response of negative-mobility particles

Understanding the fluctuations and response of particles in potential landscapes is a fundamental problem in nonequilibrium statistical physics. Here, we investigate how negative mobility reshapes the stochastic behavior of a particle moving in a mechanical potential landscape. We consider a one-dimensional overdamped particle subject to additive noise, with mobility that is negative at weak forces and positive at strong forces. In a potential well, negative mobility destabilizes the mechanical potential minimum and produces bimodal localization at two off-center positions. The same stability reversal transforms conventional Kramers escape from a potential well into a two-stage escape process involving an intermediate metastable state. When an additional spatially uniform force is applied, the mechanical perturbation translates rather than tilts the effective double well, yielding a positive response dominated at weak noise by intrawell relaxation, even though slow interwell switching dominates spontaneous positional fluctuations. These findings reveal how negative mobility reshapes the interplay among mechanical landscapes, stochastic stability, and response.