  Within the context of the Brownian ratchet model, a molecular rotary system
was studied that can perform unidirectional rotations induced by linearly
polarized ac fields, and produce positive work under loads. The model is based
on the Langevin equation for a particle in a two-dimensional (2D) three-tooth
ratchet potential of threefold symmetry. The performance of the system is
characterized by the coercive torque, i.e., the strength of the load competing
with the torque induced by the ac driving field, and the energy efficiency in
force conversion from the driving field to torque. We propose a master equation
for coarse-grained states, which takes into account boundary motion between
states, and develop a kinetic description to estimate mean angular momentum
(MAM) and powers relevant to the energy balance equation. The framework of
analysis incorporates several 2D characteristics, and is applicable to a wide
class of models of smooth 2D ratchet potential. We confirm that the obtained
expressions for MAM, power, and efficiency of the model can predict qualitative
behaviors. We also discuss the usefulness of the torque/power relationship for
experimental analyses, and propose a characteristic for 2D ratchet systems.
