Title: Experimental measurement of mean transition path velocities of colloidal particles surmounting energy barriers

Abstract: Transition paths are rare events occurring when a system, thanks to the effect of fluctuations, crosses successfully from one stable state to another by surmounting an energy barrier. Even though they are of great significance in many mesoscale processes, their direct determination is often challenging due to their short duration as compared to other relevant time-scales. Here, we measure the local average velocity along transition paths of a colloidal bead embedded in a glycerol/water mixture that hops over a barrier separating two optical potential wells. Owing to the slow dynamics of the bead in this viscous medium, we can spatially resolve the mean velocity profiles of the transition paths for distinct potentials, which agree with theoretical predictions of a model for the motion of a Brownian particle traversing a parabolic barrier. This allows us to experimentally verify various expressions linking the behavior of such mean velocities with equilibrium and transition path position distributions, mean transition-path times and mean escape times from the wells. We also show that artifacts in the mean velocity profiles arise when reducing the experimental time resolution, thus highlighting the importance of the sampling rate in the characterization of the transition path dynamics. Our results confirm that mean transition path velocity establishes a fundamental relationship between mean transition path times and equilibrium rates in thermally activated processes of small-scaled systems.