A simple two-dimensional (2D) model of the Feynman-Smoluchowski ratchet is studied. Motion of the wheel, driven by stochastic hits of the surrounding molecules, is described as diffusion along the longitudinal coordinate $x$; the stochastic motion of the pawl is represented in the transverse coordinate $y$. Different temperatures of the reservoirs connected to the particular degrees of freedom, together with asymmetry of the energetic landscape of the system, give rise to the ratchet effect. We apply mapping of the corresponding 2D Fokker-Planck equation onto the longitudinal coordinate $x$. The mapped 1D equation is of the generalized Fick-Jacobs type with an effective potential containing a part increasing or decreasing with $x$, connected with vorticity of the scaled driving force and the stationary probability current. It is responsible for the final rectified motion in the longitudinal direction.

• Received 28 June 2018

DOI:https://doi.org/10.1103/PhysRevE.98.042141