# Thermal ratchet effect in confining geometries

## TL;DR

This paper presents a stochastic model of the Feynman-Smoluchowski ratchet, solved with a generalized Fick-Jacobs theory, revealing nonlinear responses and performance metrics in confining geometries.

## Contribution

It introduces a generalized theoretical framework for analyzing the ratchet effect in confined geometries, including nonlinear response and performance quantification.

## Key findings

- The theory accurately predicts ratchet behavior compared to numerical simulations.
- The model links probability current rotations to the direction of mean velocity.
- Performance metrics like mean velocity and heat flow are quantitatively analyzed.

## Abstract

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.