  We study the trajectories of a single colloidal particle as it hops between
two energy wells A and B, which are sculpted using adjacent optical traps by
controlling their respective power levels and separation. Whereas the dynamical
behaviors of such systems are often treated by master-equation methods that
focus on particles as actors, we analyze them here instead using a
trajectory-based variational method called Maximum Caliber, which utilizes a
dynamical partition function. We show that the Caliber strategy accurately
predicts the full dynamics that we observe in the experiments: from the
observed averages, it predicts second and third moments and covariances, with
no free parameters. The covariances are the dynamical equivalents of
Maxwell-like equilibrium reciprocal relations and Onsager-like dynamical
relations. In short, this work describes an experimental model system for
exploring full trajectory distributions in one-particle two-state systems, and
it validates the Caliber approach as a useful way to understand
trajectory-based dynamical distribution functions in this system.
