The triumph of heat engines is their ability to convert the disordered energy of thermal sources into useful mechanical motion. In recent years, much effort has been devoted to generalizing thermodynamic notions to the quantum regime, partly motivated by the promise of surpassing classical heat engines. Here, we instead adopt a bottom-up approach: we propose a realistic autonomous heat engine that can serve as a testbed for quantum effects in the context of thermodynamics. Our model draws inspiration from actual piston engines and is built from closed-system Hamiltonians and weak bath coupling terms. We analytically derive the performance of the engine in the classical regime via a set of nonlinear Langevin equations. In the quantum case, we perform numerical simulations of the master equation. Finally, we perform a dynamic and thermodynamic analysis of the engine's behaviour for several parameter regimes in both the classical and quantum case, and find that the latter exhibits a consistently lower efficiency due to additional noise.

13 pages, 8 figures; added a thermodynamic analysis of the engine's performance