A colloidal particle in a time-varying harmonic trap acts as a Brownian heat engine when coupled alternately to hot and cold reservoirs. Stochastic thermodynamics tracks work W and heat Q along individual trajectories. Efficiency at maximum power follows the Curzon-Ahlborn bound η_CA = 1−√(Tc/Th), below Carnot.
Jarzynski: ⟨e^{−W/kT}⟩ = e^{−ΔF/kT}
Crooks: P(W)/P̃(−W) = e^{(W−ΔF)/kT}
η_CA = 1−√(Tc/Th) (at max power)
η ≤ η_C = 1−Tc/Th (Carnot bound)
σ = ⟨W⟩/Th − ⟨Q_c⟩/Tc ≥ 0