Finite-time quantum Stirling heat engine

TL;DR

This paper analyzes the thermodynamic performance of a finite-time quantum Stirling heat engine with a two-level system, revealing how driving speed and time scales influence efficiency and power, and proposing new optimization strategies.

Contribution

It introduces a non-Markovian master equation for finite-time quantum cycles and explores how driving speeds affect efficiency and power in a quantum heat engine.

Findings

Driving at resonance time enhances cycle performance.

Efficiency can surpass slow adiabatic cycles but stays below Carnot.

Maximum power and efficiency can be achieved nearly simultaneously.

Abstract

We study the thermodynamic performance of the finite-time non-regenerative Stirling cycle used as a quantum heat engine. We consider specifically the case in which the working substance (WS) is a two-level system. The Stirling cycle is made of two isochoric transformations separated by a compression and an expansion stroke during which the working substance is in contact with a thermal reservoir. To describe these two strokes we derive a non-Markovian master equation which allows to study the dynamics of a driven open quantum system with arbitrary fast driving. We found that the finite-time dynamics and thermodynamics of the cycle depend non-trivially on the different time scales at play. In particular, driving the WS at a time scale comparable to the resonance time of the bath enhances the performance of the cycle and allows for an efficiency higher than the efficiency of the slow adiabatic cycle, but still below the Carnot bound. Interestingly, performance of the cycle is dependent on the compression and expansion speeds asymmetrically. This suggests new freedom in optimizing quantum heat engines. We further show that the maximum output power and the maximum efficiency can be achieved almost simultaneously, although the net extractable work declines by speeding up the drive.