Quantum unital Otto heat engines: using Kirkwood-Dirac quasi-probability for the engine's coherence to stay alive

TL;DR

This paper analyzes quantum unital Otto heat engines, focusing on how quantum coherence, quantified via Kirkwood-Dirac quasi-probability, affects work, reliability, and efficiency, with detailed analytical and comparative studies.

Contribution

It introduces a method to compute cumulants of quantum heat engines considering coherence and compares dephased and undephased engines, highlighting the role of quantum measurement.

Findings

Quantum coherence can enhance work extraction and efficiency.

Dephased and undephased engines show different performance characteristics.

Non-adiabatic transitions can sometimes improve thermodynamic quantities.

Abstract

In this work, we consider quantum unital Otto heat engines. The latter refers to the fact that both the unitaries of the adiabatic strokes and the source of the heat provided to the engine preserve the maximally mixed state. We show how to compute the cumulants of either the dephased or undephased engine. For a qubit, we give the analytical expressions of the averages and variances for arbitrary unitaries and unital channels. We do a detailed comparative study between the dephased and undephased heat engines. More precisely, we focus on the effect of the parameters on the average work and its reliability and efficiency. As a case study of unital channels, we consider a quantum projective measurement. We show on which basis we should projectively measure the qubit, either the dephased or undephased heat engine, to extract higher amounts of work, increase the latter's reliability, and increase efficiency. Further, we show that non-adiabatic transitions are not always detrimental to thermodynamic quantities. Our results, we believe, are important for heat engines fueled by quantum measurement.