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Within the context of the Brownian ratchet model, a molecular rotary systemwas studied that can perform unidirectional rotations induced by linearlypolarized ac fields, and produce positive work under loads. The model is basedon the Langevin equation for a particle in a two-dimensional (2D) three-toothratchet potential of threefold symmetry. The performance of the system ischaracterized by the coercive torque, i.e., the strength of the load competingwith the torque induced by the ac driving field, and the energy efficiency inforce conversion from the driving field to torque. We propose a master equationfor coarse-grained states, which takes into account boundary motion betweenstates, and develop a kinetic description to estimate mean angular momentum(MAM) and powers relevant to the energy balance equation. The framework ofanalysis incorporates several 2D characteristics, and is applicable to a wideclass of models of smooth 2D ratchet potential. We confirm that the obtainedexpressions for MAM, power, and efficiency of the model can predict qualitativebehaviors. We also discuss the usefulness of the torque/power relationship forexperimental analyses, and propose a characteristic for 2D ratchet systems.

Performance Estimation for Two-Dimensional Brownian Rotary Ratchet Systems