Equilibrium Theory for a Particle Pulled by a Moving Optical Trap

TL;DR

This paper demonstrates that a colloidal particle pulled by a moving optical trap can be modeled using equilibrium theory due to rapid mechanical equilibration, enabling analysis of stochastic dynamics with generalized thermodynamic concepts.

Contribution

It introduces a framework applying equilibrium theory to driven colloidal systems, extending fluctuation-dissipation and detailed balance concepts to non-equilibrium conditions.

Findings

Mechanical force equals viscous drag force in relevant time scales

Equilibrium distribution functions describe the system in the stationary frame

Generalized fluctuation-dissipation relations are derived

Abstract

The viscous drag on a colloidal particle pulled through solution by an optical trap is large enough that on experimentally relavant time scales the mechanical force exerted by the trap is equal and op- posite the viscous drag force. The rapid mechanical equilibritation allows the system to be modeled using equilibrium theory, where the effects of the energy dissipation (thermodynamic disequilibrium) show up only in the coordinate transformations that map the system from the laboratory frame of reference, relative to which the particle is moving, to a frame of reference in which the particle is, on average, stationary and on which the stochastic dynamics is governed by a canonical equilib- rium distribution function. The simple equations in the stationary frame can be analyzed using the Onsager-Machlup theory for stochastic systems and provide generalizations of equilibrium and near equilibrium concepts such as detailed balance and fluctuation-dissipation relations applicable to a wide range of systems including molecular motors, pumps, and other nano-scale machines.