  Brownian rotors play an important role in biological systems and in future
nano-technological applications. However the mechanisms determining their
dynamics, efficiency and performance remain to be characterized. Here the F0
portion of the F-ATP synthase is considered as a paradigm of a Brownian rotor.
In a generic analytical model we analyze the stochastic rotation of F0-like
motors as a function of the driving free energy difference and of the free
energy profile the rotor is subjected to. The latter is composed of the rotor
interaction with its surroundings, of the free energy of chemical transitions,
and of the workload. The dynamics and mechanical efficiency of the rotor
depends on the magnitude of its stochastic motion driven by the free energy
energy difference and its rectification on the reaction-diffusion path. We
analyze which free energy profiles provide maximum flow and how their
arrangement on the underlying reaction-diffusion path affects rectification and
-- by this -- the efficiency.
