Stochastic model of the Feynman-Smoluchowski ratchet is proposed and solvedusing generalization of the Fick-Jacobs theory. The theory fully capturesnonlinear response of the ratchet to the difference of heat bath temperatures.The ratchet performance is discussed using the mean velocity, the average heatflow between the two heat reservoirs and the figure of merit, which quantifiesenergetic cost for attaining a certain mean velocity. Limits of the theory aretested comparing its predictions to numerics. We also demonstrate connectionbetween the ratchet effect emerging in the model and rotations of theprobability current and explain direction of the mean velocity using simplediscrete analogue of the model.
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