Active Ornstein-Uhlenbeck model for bacterial heat engines

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 a single active Ornstein-Uhlenbeck particle (AOUP), effectively representing the whole many-body setup. Due to the probe's fast relaxation in the potential, in typical experimental implementations, good agreement can prevail even when the autocorrelation function of the active noise develops nonexponential 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.