# Non-Markovian Effects on Overdamped Systems

## TL;DR

This paper investigates how non-Markovian memory effects influence overdamped systems, revealing that weak noise can regularize equilibrium properties and coupling to another bath restores missing dynamics.

## Contribution

It demonstrates the impact of non-Markovian effects on overdamped systems and shows how external noise and bath coupling can recover equilibrium and dynamical features.

## Key findings

- Non-Markovian effects alter stationary behavior from Boltzmann-Gibbs statistics.
- Weak external white noise regularizes equilibrium properties.
- Bath coupling restores dynamical aspects lost in overdamped approximation.

## Abstract

We study the consequences of adopting the memory dependent, non-Markovian, physics with the memory-less over-damped approximation usually employed to investigate Brownian particles. Due to the finite correlation time scale associated with the noise, the stationary behavior of the system is not described by the Boltzmann-Gibbs statistics. However, the presence of a very weak external white noise can be used to regularize the equilibrium properties. Surprisingly, the coupling to another bath effectively restores the dynamical aspects missed by the over-damped treatment.