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

TL;DR

This paper demonstrates that the Maximum Caliber variational method accurately predicts the full trajectory distributions of a single colloidal particle hopping between two energy wells, validated through experiments.

Contribution

It introduces a trajectory-based variational approach, Maximum Caliber, to analyze two-state kinetics, providing accurate predictions without free parameters.

Findings

Maximum Caliber predicts experimental trajectory moments and covariances.

Covariances follow Maxwell-like reciprocal relations and Onsager-like dynamical relations.

The approach validates trajectory distribution analysis in single-particle two-state systems.

Abstract

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.