We discuss twodimensional diffusion of a Brownian particle confined to a periodic asymmetric channel with soft walls modeled by a parabolic potential. In the channel, the particle experiences different thermal noise intensities, or temperatures, in the transversal and longitudinal directions.The model is inspired by the famous Feynman's ratchet and pawl. Although the standard FickJacobs approximation predicts correctly the effective diffusion
coeffcient, it fails to capture the ratchet effect. Deriving a correction, which breaks the local detailed balance with the transversal noise source, we obtain a
correct mean velocity of the particle and a stationary probability density in the potential unit cell. The derived results are exact for small channel width. Yet, we check by exact numerical calculation that they qualitatively describe the ratchet effect observed for an arbitrary width of the channel.
Download TeX format
