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We study the trajectories of a single colloidal particle as it hops betweentwo energy wells A and B, which are sculpted using adjacent optical traps bycontrolling their respective power levels and separation. Whereas the dynamicalbehaviors of such systems are often treated by master-equation methods thatfocus on particles as actors, we analyze them here instead using atrajectory-based variational method called Maximum Caliber, which utilizes adynamical partition function. We show that the Caliber strategy accuratelypredicts the full dynamics that we observe in the experiments: from theobserved averages, it predicts second and third moments and covariances, withno free parameters. The covariances are the dynamical equivalents ofMaxwell-like equilibrium reciprocal relations and Onsager-like dynamicalrelations. In short, this work describes an experimental model system forexploring full trajectory distributions in one-particle two-state systems, andit validates the Caliber approach as a useful way to understandtrajectory-based dynamical distribution functions in this system.

A trajectory approach to two-state kinetics of single particles on sculpted energy landscapes