  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.
