Self-consistency of optimizing finite-time Carnot engines with the low-dissipation model

TL;DR

This paper investigates the validity of the low-dissipation model's assumptions for finite-time Carnot engines, revealing it is only self-consistent at low Carnot efficiencies and can underestimate efficiency at higher efficiencies.

Contribution

It demonstrates the limitations of the low-dissipation model for high Carnot efficiencies using a two-level atomic heat engine example.

Findings

The model is self-consistent only when Carnot efficiency is very low.

At higher efficiencies, the actual EMP exceeds the bound predicted by the model.

The validity of the inverse proportionality assumption depends on the efficiency regime.

Abstract

The efficiency at the maximum power (EMP) for finite-time Carnot engines established with the low-dissipation model, relies significantly on the assumption of the inverse proportion scaling of the irreversible entropy generation $\Delta S^{(\mathrm{ir})}$ on the operation time $\tau$, i.e., $\Delta S^{(\mathrm{ir})}\propto1/\tau$. The optimal operation time of the finite-time isothermal process for EMP has to be within the valid regime of the inverse proportion scaling. Yet, such consistency was not tested due to the unknown coefficient of the $1/\tau$-scaling. In this paper, using a two-level atomic heat engine as an illustration, we reveal that the optimization of the finite-time Carnot engines with the low-dissipation model is self-consistent only in the regime of $\eta_{\mathrm{C}}\ll1$, where $\eta_{\mathrm{C}}$ is the Carnot efficiency. In the large-$\eta_{\mathrm{C}}$ regime, the operation time for EMP obtained with the low-dissipation model is not within the valid regime of the $1/\tau$-scaling, and the exact EMP is found to surpass the well-known bound $\eta_{+}=\eta_{\mathrm{C}}/(2-\eta_{\mathrm{C}})$