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Stochastic motion of particles in a highly unstable potential generates anumber of diverging trajectories leading to undefined statistical moments ofthe particle position. This makes experiments challenging and breaks down astandard statistical analysis of unstable mechanical processes and theirapplications. A newly proposed approach takes advantage of the localcharacteristics of the most probable particle motion instead of the divergentaverages. We experimentally verify its theoretical predictions for a Brownianparticle moving near an inflection in a highly unstable cubic opticalpotential. The most-likely position of the particle atypically shifts againstthe force despite the trajectories diverge in the opposite direction. The localuncertainty around the most-likely position saturates even for strong diffusionand enables well-resolved position detection. Remarkably, the measured particledistribution quickly converges to the quasi-stationary one with the sameatypical shift for different initial particle positions. The demonstratedexperimental confirmation of the theoretical predictions approves the utilityof local characteristics for highly unstable systems which can be exploited inthermodynamic processes to uncover energetics of unstable systems.

Diffusing Up the Hill: Dynamics and Equipartition in Highly Unstable Systems