# Brownian ratchets: How stronger thermal noise can reduce diffusion

## TL;DR

This paper investigates how increasing thermal noise can paradoxically decrease diffusion in a Brownian motor on a ratchet substrate, revealing a non-monotonic relationship influenced by temperature.

## Contribution

It demonstrates the non-monotonic dependence of diffusion on temperature in a Brownian ratchet system and explains the suppression of diffusion through a three-state stochastic model.

## Key findings

- Diffusion coefficient exhibits a non-monotonic dependence on temperature.
- Thermal noise can suppress diffusion in certain temperature ranges.
- A three-state stochastic model explains the diffusion suppression phenomenon.

## Abstract

We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e. a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force which takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum and finally it monotonically increases in accordance with the Einstein linear relation. Particularly interesting is the temperature interval in which diffusion is suppressed by thermal noise and we explain this effect in terms of transition rates of a three-state stochastic model.