Experimental Measurement of Relative Path Probabilities and Stochastic Actions

Abstract

For diffusive stochastic dynamics, the probability to observe any individual trajectory is vanishingly small, making it unclear how to experimentally validate theoretical results for ratios of path probabilities. We provide the missing link between theory and experiment, by establishing a protocol to extract ratios of path probabilities from measured time series without fitting a model. For experiments on a single colloidal particle in a microchannel, we extract both ratios of path probabilities, and the most probable path for a barrier crossing. While we find excellent agreement with independently calculated predictions based on the Onsager-Machlup stochastic action, our experimental results are inconsistent with the Freidlin-Wentzell stochastic action. The direct experimental measurement of relative path probabilities presented here paves the way for experimental investigation of any theoretical result related to individual stochastic trajectories.