Entropy-based analysis of single-qubit Otto and Carnot heat engines

TL;DR

This paper uses an entropy-based approach to analyze quantum heat engines with a single qubit, revealing how coherence and entropy generation impact their efficiency and irreversibility.

Contribution

It introduces an entropy-based formulation of the first law in quantum thermodynamics, including coherence work, and analyzes the efficiency bounds of quantum Otto and Carnot engines.

Findings

Carnot cycle achieves classical Carnot efficiency.

Otto cycle's efficiency is bounded by Carnot efficiency at extreme temperatures.

Entropy generation during isochoric stages limits Otto cycle efficiency.

Abstract

From an entropy-based formulation of the first law of thermodynamics in the quantum regime, we investigate the performance of Otto-like and Carnot-like engines for a single-qubit working medium. Within this framework, the first law includes an additional contribution -- coherence work -- that quantifies the energetic cost of deviating the quantum trajectory from its natural unitary evolution. We focus on the efficiency of the heat-to-coherence work conversion and show that the Carnot cycle achieves the classical Carnot efficiency, while the performance of the Otto cycle is upper-bounded by the Carnot efficiency corresponding to the extreme temperatures of the cycle. We identify entropy generation during the isochoric stages as the key source of irreversibility limiting the Otto cycle's efficiency.