Thermodynamic performance of a quantum Stirling heat engine with a single particle confined in a cubic potential well

This study investigates the thermodynamic performance of a three-dimensional quantum Stirling heat engine (QSHE), which operates through two isothermal and two isochoric processes, with a single particle confined within a cubic potential well. The thermodynamic model accounts for the degeneracy of energy levels. The effects of compression ratio, temperature ratio, and particle mass on the work output, thermal efficiency, and regeneration heat transfer are analyzed. These results provide a basis for a qualitative comparison with macroscopic Stirling heat engines (MSHEs). For the electron-based QSHE, there exists a strip where the thermal efficiency exceeds the Carnot efficiency. This strip divides the graph into two regions on either side with thermal efficiencies lower than the Carnot efficiency. The region with efficiency lower than Carnot on the right tends to expand as the compression ratio $\mathrm{CR}$ and the temperature ratio $\gamma$ increase. The dimensionless work output $W_{\mathrm{net}}^{*}$ increases with temperature ratio, compression ratio, and dimensionless cooling temperature, similar to trends observed in ideal MSHEs. The maximum values of $W_{\mathrm{net}}^{*}$ are 2.63, 7.87, 13.08, and 18.27 at the respective optimal points $\left(a^{*},\mathrm{CR},\gamma \right)$ = (1.07, 5.0, 1.5), (0.97, 5.0, 2.5), (0.90, 5.0, 3.5), and (0.85, 5.0, 4.5). Similar to practical MSHEs, the QSHE achieves higher dimensionless thermal efficiency ${\eta }^{*}$ and work output $W_{\mathrm{net}}^{*}$ when the working particle has a smaller mass. In particular, the maximum $W_{\mathrm{net}}^{*}$ of the electron-based QSHE is two orders of magnitude greater than that of the proton-based QSHE.