Active Ornstein-Uhlenbeck Model for Bacterial Heat Engines

TL;DR

This paper demonstrates that an active Ornstein-Uhlenbeck process effectively models the stochastic thermodynamics of bacterial heat engines with colloidal probes in active baths, providing analytical insights into their efficiency and work distributions.

Contribution

It introduces an AOUP-based effective model for bacterial heat engines, capturing their stochastic behavior under experimentally relevant conditions.

Findings

Gaussian active noise with exponential autocorrelation at intermediate activities

Effective AOUP model accurately predicts work, heat, and efficiency distributions

Good agreement persists even with non-exponential autocorrelation tails

Abstract

We use Brownian dynamics simulations to study a model of a cyclic bacterial heat engine based on a harmonically confined colloidal probe particle in a bath formed by active Brownian particles. For intermediate activities, active noise experienced by large enough probes becomes Gaussian with exponential autocorrelation function. We show that, in this experimentally pertinent regime, the probability densities for stochastic work, heat, and efficiency are well represented by those of an effective active Ornstein-Uhlenbeck particle (AOUP). Due to the probe's fast relaxation in the potential in typical experimental implementations, good agreement can prevail even when the noise autocorrelation function develops non-exponential tails. Our results show that the AOUP provides a convenient and accurate, analytically tractable effective model to mimic and analyze experimental bacterial heat engines, especially when operating with comparatively large probes and stiff traps.