Escape rate of active particles in the effective equilibrium approach

TL;DR

This paper develops an effective equilibrium approach to accurately predict the escape rate of active particles over potential barriers, bridging the gap between out-of-equilibrium activity and classical Kramers theory.

Contribution

It introduces an effective potential method for active particles, enabling the use of Kramers theory to predict escape rates with high accuracy.

Findings

Effective potential approach matches simulation data well.

Analytical results agree with numerical simulations.

Method extends classical theory to active matter systems.

Abstract

The escape rate of a Brownian particle over a potential barrier is accurately described by the Kramers theory. A quantitative theory explicitly taking the activity of Brownian particles into account has been lacking due to the inherently out-of-equilibrium nature of these particles. Using an effective equilibrium approach [Farage et al., Phys. Rev. E 91, 042310 (2015)] we study the escape rate of active particles over a potential barrier and compare our analytical results with data from direct numerical simulation of the colored noise Langevin equation. The effective equilibrium approach generates an effective potential which, when used as input to Kramers rate theory, provides results in excellent agreement with the simulation data.