Quantum engine efficiency bound beyond the second law of thermodynamics

Wolfgang Niedenzu,Victor Mukherjee,Abraham G Kofman,Gershon Kurizki,Arnab Ghosh

doi:10.1038/s41467-017-01991-6

Wolfgang Niedenzu, Victor Mukherjee + Show 3 more

Open Access

https://doi.org/10.1038/s41467-017-01991-6

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Abstract

According to the second law, the efficiency of cyclic heat engines is limited by the Carnot bound that is attained by engines that operate between two thermal baths under the reversibility condition whereby the total entropy does not increase. Quantum engines operating between a thermal and a squeezed-thermal bath have been shown to surpass this bound. Yet, their maximum efficiency cannot be determined by the reversibility condition, which may yield an unachievable efficiency bound above unity. Here we identify the fraction of the exchanged energy between a quantum system and a bath that necessarily causes an entropy change and derive an inequality for this change. This inequality reveals an efficiency bound for quantum engines energised by a non-thermal bath. This bound does not imply reversibility, unless the two baths are thermal. It cannot be solely deduced from the laws of thermodynamics.

Highlights

According to the second law, the efficiency of cyclic heat engines is limited by the Carnot bound that is attained by engines that operate between two thermal baths under the reversibility condition whereby the total entropy does not increase
This corresponds to the minimum amount of heat being dumped into the cold bath, so as to close the cycle, and to the maximum input heat being transformed into work
In an irreversible cycle, a larger amount of heat must be dumped into the cold bath, so that less input heat is available for conversion into work, causing the engine efficiency to decrease[3, 5]

Summary

Introduction

According to the second law, the efficiency of cyclic heat engines is limited by the Carnot bound that is attained by engines that operate between two thermal baths under the reversibility condition whereby the total entropy does not increase. While mechanical engines may reach this bound, Carnot showed[1] that the efficiency of any heat engine that cyclically operates between two thermal baths is universally limited by the ratio of the bath temperatures, regardless of the concrete design[2, 3] The universality of this bound led to the introduction of the notion of entropy by Clausius[4] and the formalisation of the second law of thermodynamics. A distinction is to be drawn between two types of non-thermal engines[32, 36], (i) engines wherein the working medium equilibrates to a thermal state whose temperature is adjustable (e.g., by the phase of the coherence in a ‘phaseonium’ bath10), which qualify as genuine heat engines with a controllable Carnot bound, and (ii) engines wherein the non-thermal (e.g., squeezed30) bath may render the working-medium state non-thermal, making the Carnot bound irrelevant

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