Quantum Heat Machines Equivalence, Work Extraction beyond Markovianity, and Strong Coupling via Heat Exchangers

Uzdin, Raam; Levy, Amikam; Kosloff, Ronnie

doi:10.3390/e18040124

Cited by 77 publications

(84 citation statements)

References 86 publications

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“…In the equivalence regime these machines still have entirely different dynamics, yet their thermodynamics features are the same. This result was recently extended to the non-Markovian regime where the machine and the bath are strongly coupled [56]. For other studies of coherence in quantum heat engines see [41,[57][58][59].…”

Section: Introductionmentioning

confidence: 82%

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Coherence-Induced Reversibility and Collective Operation of Quantum Heat Machines via Coherence Recycling

Uzdin

2016

Phys. Rev. Applied

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102

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Collective behavior where a set of elements interact and generate effects that are beyond the reach of the individual non interacting elements, are always of great interest in physics. Quantum collective effects that have no classical analogue are even more intriguing. In this work we show how to construct collective quantum heat machines and explore their performance boosts with respect to regular machines. Without interactions between the machines the individual units operate in a stochastic, non-quantum manner. The construction of the collective machine becomes possible by introducing two simple quantum operations: coherence extraction and coherence injection. Together these operations can harvest coherence from one engine and use it to boost the performance of a slightly different engine. For weakly driven engines we show that the collective work output scales quadratically with the number of engines rather than linearly. Eventually, the boost saturates and the scaling becomes linear. Nevertheless, even in saturation, work is still significantly boosted compared to individual operation. To study the reversibility of the collective machine we introduce the 'entropy pollution' measure. It is shown that there is a regime where the collective machine is N times more reversible while producing N times more work, compared to the individual operation of N units. Moreover, the collective machine can even be more reversible than the most reversible unit in the collective. This high level of reversibility becomes possible due to a special symbiotic mechanism between engine pairs.

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Section: Introductionmentioning

confidence: 82%

“…This is experimentally and theoretically well motivated in a wide range of physical systems in atomic physics. Some studies replace the classical field by a quantum battery (work repository) [36,56,60,76,77]. This is very interesting, and deserves further study.…”

Section: Introductionmentioning

confidence: 99%

Coherence-Induced Reversibility and Collective Operation of Quantum Heat Machines via Coherence Recycling

Uzdin

2016

Phys. Rev. Applied

Self Cite

102

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“…Purely quantum effects in quantum heat engine were discussed in Refs. [489,490]: stationary, twoand four-stroke quantum Otto engines perform equivalently when the operator norm of the time-evolution operator is much smaller than the Planck constant. This becomes possible for few-level quantum systems.…”

Section: Cyclic Quantum Engines and Quantum Coherence Effectsmentioning

confidence: 99%

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

et al. 2017

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In recent years, the study of heat to work conversion has been re-invigorated by nanotechnology. Steady-state devices do this conversion without any macroscopic moving parts, through steady-state flows of microscopic particles such as electrons, photons, phonons, etc. This review aims to introduce some of the theories used to describe these steady-state flows in a variety of mesoscopic or nanoscale systems. These theories are introduced in the context of idealized machines which convert heat into electrical power (heat-engines) or convert electrical power into a heat flow (refrigerators). In this sense, the machines could be categorized as thermoelectrics, although this should be understood to include photovoltaics when the heat source is the sun. As quantum mechanics is important for most such machines, they fall into the field of quantum thermodynamics. In many cases, the machines we consider have few degrees of freedom, however the reservoirs of heat and work that they interact with are assumed to be macroscopic. This review discusses different theories which can take into account different aspects of mesoscopic and nanoscale physics, such as coherent quantum transport, magnetic-field induced effects (including topological ones such as the quantum Hall effect), and single electron charging effects. It discusses the efficiency of thermoelectric conversion, and the thermoelectric figure of merit. More specifically, the theories presented are (i) linear response theory with or without magnetic fields, (ii) Landauer scattering theory in the linear response regime and far from equilibrium, (iii) Green-Kubo formula for strongly interacting systems within the linear response regime, (iv) rate equation analysis for small quantum machines with or without interaction effects, (v) stochastic thermodynamic for fluctuating small systems. In all cases, we place particular emphasis on the fundamental questions about the bounds on ideal machines. Can magnetic-fields change the bounds on power or efficiency? What is the relationship between quantum theories of transport and the laws of thermodynamics? Does quantum mechanics place fundamental bounds on heat to work conversion which are absent in the thermodynamics of classical systems?

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“…Furthermore, considering a probabilistic approach towards work extraction, [20] found that the achievement of CE is very unlikely, when considering energy fluctuations in the microregime.Can we design a QHE that operates between genuinely thermal reservoirs and yet achieves a high efficiency 5 ? To answer this, several protocols have been proposed and analyzed [9,11,17,[22][23][24][25][26][27], some showing QHEs that operate at the CE [9, 27, 28]. However, crucial to these results is the definition of work.…”

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confidence: 99%

Surpassing the Carnot efficiency by extracting imperfect work

Woods

Wehner

2017

New J. Phys.

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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. Recently, a number of schemes for QHEs have been proposed and analyzed, involving systems such as ion traps, photocells, or optomechanical systems [2][3][4][5][6][7][8][9][10]. Some of these schemes lie outside the usual heat engine setting (see figure 1). For example, instead of using a hot and cold bath, the extended quantum heat engine (EQHE) has access to reservoirs which are not in a thermal state [3,11,12]. In this case, EQHE with high efficiencies (even surpassing h C ) have been proposed and demonstrated. Nevertheless, [13] has pointed out that the second law is, strictly speaking, never violated because one always has to invest extra work in order to create and replenish these non-thermal reservoirs. Nevertheless, the study of using such non-thermal reservoirs can still be of interest, since they potentially may boost other features of the heat engine, such as the rate of extracting work. However, in this manuscript we are focusing on the standard setting of a QHE, in which the baths are thermal, where in classical thermodynamics, it is proven that although CE can be approached, it can never be surpassed [14].Even without additional resources such as those in EQHEs, QHEs are already radically different from classical engines, since energy fluctuations are much more prominent due to the small number of particles involved. The laws of thermodynamics for small quantum systems are more restrictive due to finite-size effects [14][15][16][17][18][19]. It is known that such second laws introduce additional restrictions on the performance of QHEs [14]. Specifically, not all QHEs can even achieve the CE. The maximal achievable efficiency depends not only on the temperatures, but also on the Hamiltonian structure of the baths involved. Furthermore, considering a probabilistic approach towards work extraction, [20] found that the achievement of CE is very unlikely, when considering energy fluctuations in the microregime.Can we design a QHE that operates between genuinely thermal reservoirs and yet achieves a high efficiency 5 ? To answer this, several protocols have been propos...

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Quantum Heat Machines Equivalence, Work Extraction beyond Markovianity, and Strong Coupling via Heat Exchangers

Cited by 77 publications

References 86 publications

Coherence-Induced Reversibility and Collective Operation of Quantum Heat Machines via Coherence Recycling

Coherence-Induced Reversibility and Collective Operation of Quantum Heat Machines via Coherence Recycling

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

Surpassing the Carnot efficiency by extracting imperfect work

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