Resolution dependence of most probable pathways with state-dependent diffusivity

Recent experiments have probed the relative likelihoods of trajectories in stochastic systems by observing survival probabilities within a tube of radius R in spacetime. We measure such probabilities here for a colloidal particle in a corrugated channel, corresponding to a bistable potential with state-dependent diffusivity. In contrast to previous findings for state-independent noise, we find that the most probable pathway changes qualitatively as the tube radius R is altered. We explain this by computing the survival probabilities predicted by overdamped Langevin dynamics. At high enough resolution (small enough R), survival probabilities depend solely on diffusivity variations, independent of deterministic forces; finite R corrections yield a generalization of the Onsager-Machlup action. As corollary, ratios of survival probabilities are singular as R → 0, but become regular, and described by the classical Onsager-Machlup action, only in the special case of state-independent noise.