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arXiv:2110.04550

Works with quantum resource of coherence

Yuhan Ma, Liu, C. L., C. P. Sun

Published Oct 9, 2021• 2 citations
arXivHTMLPDF

Abstract

We study the modification of the second law of thermodynamics for a quantum system interacting with a reservoir regarding quantum coherence. The whole system is isolated so that neither energy nor information is lost. It is discovered that the coherence of the reservoir can serves as a useful resource allowing the system extract more energy from the reservoir; among the coherence measures, only is the relative entropy of coherence feasible to quantitatively characterize energy exchange. We demonstrate that a thermodynamic cycle between two coherent reservoirs can output more work than its classical counterpart. The efficiency of such cycle surpasses the Carnot efficiency, which is the upper bound of heat engine efficiency in classical regime.

DOI
10.48550/arxiv.2110.04550

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We study the modification of the second law of thermodynamics for a quantum system interacting with a reservoir regarding quantum coherence. The whole system is isolated so that neither energy nor information is lost. It is discovered that the coherence of the reservoir can serves as a useful resource allowing the system extract more energy from the reservoir; among the coherence measures, only is the relative entropy of coherence feasible to quantitatively characterize energy exchange. We demonstrate that a thermodynamic cycle between two coherent reservoirs can output more work than its classical counterpart. The efficiency of such cycle surpasses the Carnot efficiency, which is the upper bound of heat engine efficiency in classical regime.
We investigate, in an analytical fashion, quantum Carnot cycles of a microscopic heat engine coupled to two nite heat reservoirs, whose internal cycles could own higher e ciency than the standard Carnot limit without consuming extra quantum resources, e.g., coherence or squeezing properties. The engine runs time-dependently, involving both the internal and external cycles to collaboratively accomplish a complete Carnot cycle, and the e ciency of the engine depends on the reservoirs heat capacities and the working substance. Our analytical results of the maximum efficiency and the maximum power output clarify the mechanism behind the high performance of the microscopic engines, displaying the key roles played by the nite-sized heat reservoirs. Our proposal is generally valid for any microscopic thermodynamic system and fully feasible under current laboratory conditions.
A suitable way of quantifying work for microscopic quantum systems has been constantly debated in the field of quantum thermodynamics. One natural approach is to measure the average increase in energy of an ancillary system, called the battery, after a work extraction protocol. The quality of energy extracted is usually argued to be good by quantifying higher moments of the energy distribution, or by restricting the amount of entropy to be low. This limits the amount of heat contribution to the energy extracted, but does not completely prevent it. We show that the definition of 'work' is crucial. If one allows for a definition of work that tolerates a non-negligible entropy increase in the battery, then a small scale heat engine can possibly exceed the Carnot efficiency. This can be done without using any additional resources such as coherence or correlations, and furthermore can be achieved even when one of the heat baths is finite in size.
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.
Abstract The introduction of the quantum analogue of a Carnot engine based on a bath comprising of particles with a small amount of coherence initiated an active line of research on the harnessing of different quantum resources for the enhancement of thermal machines beyond the standard reversible limit, with an emphasis on non-thermal baths containing quantum coherence. In our work, we investigate the impact of coherence on the thermodynamic tasks of a collision model which is composed of a system interacting, in the continuous time limit, with a series of coherent ancillas of two baths at different temperatures. Our results show the advantages of utilising coherence as a resource in the operation of the machine, and allows it: (a) to exhibit unconventional behaviour such as the appearance of a hybrid refrigerator, capable of simultaneous refrigeration and generation of work, and (b) to function as an engine or a refrigerator with efficiencies larger than the Carnot bound. Moreover, we find an effective upper bound to the efficiency of the thermal machine operating as an engine in the presence of a coherent reservoir.
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.
We design a heat engine with multiheat reservoir, an ancillary system, and quantum memory. We then derive an inequality related to the second law of thermodynamics and give a limitation on the work gain from the engine by analyzing the entropy change and quantum mutual information change during the process. In addition, remarkably, by the combination of two independent engines and with the help of the entropic uncertainty relation with quantum memory, we find that the total maximum work gained from those two heat engines should be larger than a quantity related to the quantum entanglement between the ancillary state and the quantum memory. This result provides a lower bound for the maximum work extracted, in contrast to the upper bound in the conventional second law of thermodynamics. However, the validity of this inequality depends on whether the maximum work can achieve the upper bound.