Optimal performance of a heat engine for a parallelly connected two quantum dots

In this paper, we developed a model of a heat engine that consists of two single-level quantum dots that are coupled in parallel and sandwiched between two thermal reservoirs with varying chemical potentials and temperatures. The difference in chemical potential and temperature facilitates the cyclical movement of electrons and acts as a heat engine. We investigate how thermodynamic quantities like heat, work, and efficiency are evaluated as a function of scaled energy. We also carried out analytical and numerical solutions for optimum scaled energies and the corresponding optimum efficiency of the thermoelectric heat engine. Therefore, the two optimum efficiencies are constrained below by the efficiency at maximum power output (eta & lowast;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta <^>*$$\end{document}), the Curzon-Ahlborn efficiency (eta CA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta _{CA}$$\end{document}), and above by the Carnot efficiency (eta C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta _C$$\end{document}). Besides, we assess the overall optimal performance of a heat engine by introducing a figure of merit. Based on the proposed figure of merit, our result shows that the second optimization criteria exhibits superior performance compared to the first optimization criteria across the full range of Carnot efficiency.