Nonequilibirum steady state for harmonically-confined active particles

TL;DR

This paper investigates the nonequilibrium steady state distribution of a harmonically confined active particle with short correlation time noise, revealing a non-Boltzmann large deviation form and deriving an exact expression for telegraphic noise.

Contribution

It provides an exact large deviation function for the steady state of an active particle under harmonic confinement with telegraphic noise, extending understanding of nonequilibrium distributions.

Findings

Large deviations follow a non-Boltzmann distribution with exponential scaling.

Derived an exact expression for the large deviation function for telegraphic noise.

Showed the effective temperature governs typical fluctuations, but large deviations differ significantly.

Abstract

We study the full nonequilibirum steady state distribution $P_{\text{st}}\left(X\right)$ of the position $X$ of a damped particle confined in a harmonic trapping potential and experiencing active noise, whose correlation time $\tau_c$ is assumed to be very short. Typical fluctuations of $X$ are governed by a Boltzmann distribution with an effective temperature that is found by approximating the noise as white Gaussian thermal noise. However, large deviations of $X$ are described by a non-Boltzmann steady-state distribution. We find that, in the limit $\tau_c \to 0$, they display the scaling behavior $P_{\text{st}}\left(X\right)\sim e^{-s\left(X\right)/\tau_{c}}$, where $s\left(X\right)$ is the large-deviation function. We obtain an expression for $s\left(X\right)$ for a general active noise, and calculate it exactly for the particular case of telegraphic (dichotomous) noise.