  Stochastic model of the Feynman-Smoluchowski ratchet is proposed and solved
using generalization of the Fick-Jacobs theory. The theory fully captures
nonlinear response of the ratchet to the difference of heat bath temperatures.
The ratchet performance is discussed using the mean velocity, the average heat
flow between the two heat reservoirs and the figure of merit, which quantifies
energetic cost for attaining a certain mean velocity. Limits of the theory are
tested comparing its predictions to numerics. We also demonstrate connection
between the ratchet effect emerging in the model and rotations of the
probability current and explain direction of the mean velocity using simple
discrete analogue of the model.
