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Coherence recycling, collective operation, and coherence induced reversibility in quantum heat engines

Raam Uzdin

Published Sep 21, 2015• 2 citations
OpenAlex

Abstract

Abstract When quantum heat engines or refrigerators operate in the over-thermalization regime, quantum effects are not expected as the thermal baths eliminates all coherences. In this work we show that even in this seemingly non-quantum regime, it is possible to harvest coherence before it is erased, and obtain non classical effects. While the engine is not affected by the coherence harvesting, the extracted coherence can be used to cool external particles and reduce their entropy (the energy of the auxiliary particles is not modified). On top of cooling the extracted coherence can activate passive states. Coherence extraction also has an impact on the basic theory of heat machines. With coherence extraction, the standard expression for the total entropy production -Qc/Tc-Qh/Th is replaced by a simple relative entropy expression, that is orders of magnitude smaller in the regime of interest. Consequently, coherence extraction enables reversibility that is otherwise impossible. In addition, we present a collective engine operation scheme where coherence is recycled and shared between engines. This leads to an interesting performance boost where the total power scales quadratically with the number of engines, rather than linearly. Finally, a scheme for resource accounting is presented. It is demonstrated that coherence extraction and coherence injection extend the scope of known quantum thermal machines and add new modes of operation.

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In $c\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}v\phantom{\rule{0}{0ex}}e$ $o\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}s$, units interact to generate synergistic effects beyond what the individual, noninteracting units could yield. A quantum collective with no classical analogue is even more intriguing. In the context of quantum thermodynamics, the authors use the concept of extracting and injecting $c\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}h\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}e$ to envision a collective heat machine of the same efficiency as its individual engines, yet drawing more heat from thermal baths and producing more work, its power scaling quadratically with the number of engines. Surprisingly, the collective machine can be more reversible than its most reversible element.

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Abstract When quantum heat engines or refrigerators operate in the over-thermalization regime, quantum effects are not expected as the thermal baths eliminates all coherences. In this work we show that even in this seemingly non-quantum regime, it is possible to harvest coherence before it is erased, and obtain non classical effects. While the engine is not affected by the coherence harvesting, the extracted coherence can be used to cool external particles and reduce their entropy (the energy of the auxiliary particles is not modified). On top of cooling the extracted coherence can activate passive states. Coherence extraction also has an impact on the basic theory of heat machines. With coherence extraction, the standard expression for the total entropy production -Qc/Tc-Qh/Th is replaced by a simple relative entropy expression, that is orders of magnitude smaller in the regime of interest. Consequently, coherence extraction enables reversibility that is otherwise impossible. In addition, we present a collective engine operation scheme where coherence is recycled and shared between engines. This leads to an interesting performance boost where the total power scales quadratically with the number of engines, rather than linearly. Finally, a scheme for resource accounting is presented. It is demonstrated that coherence extraction and coherence injection extend the scope of known quantum thermal machines and add new modes of operation.
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.
In $c\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}v\phantom{\rule{0}{0ex}}e$ $o\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}s$, units interact to generate synergistic effects beyond what the individual, noninteracting units could yield. A quantum collective with no classical analogue is even more intriguing. In the context of quantum thermodynamics, the authors use the concept of extracting and injecting $c\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}h\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}e$ to envision a collective heat machine of the same efficiency as its individual engines, yet drawing more heat from thermal baths and producing more work, its power scaling quadratically with the number of engines. Surprisingly, the collective machine can be more reversible than its most reversible element.
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.
Quantum coherence has been shown to impact the operational capabilities of quantum systems performing thermodynamic tasks in a significant way, and yet the possibility and conditions for genuine coherence-enhanced thermodynamic operation remain unclear. Introducing a comparison with classical machines using the same set of thermodynamic resources, we show that for steady-state quantum thermal machines – both autonomous and externally driven – that interact weakly with thermal reservoirs and work sources, the presence of coherence induced by perturbations in the machine Hamiltonian guarantees a genuine thermodynamic advantage under mild conditions. This advantage applies to both cases where the induced coherence is between levels with different energies or between degenerate levels. On the other hand, we show that engines subjected to noise-induced coherence can be outperformed by classical stochastic engines using exactly the same set of (incoherent) resources. We illustrate our results with three prototypical models of heat engines and refrigerators: the three-level amplifier, the three-qubit autonomous refrigerator, and a noise-induced-coherence machine.
Abstract Understanding how coherence of quantum systems affects thermodynamic quantities, such as work and heat, is essential for harnessing quantumness effectively in thermal quantum technologies. Here, we study the unique contributions of quantum coherence among different subsystems of a multipartite system, specifically in non-equilibrium steady states, to work and heat currents. Our system comprises two coupled ensembles, each consisting of N particles, interacting with two baths of different temperatures, respectively. The particles in an ensemble interact with their bath either simultaneously or sequentially, leading to non-local dissipation and enabling the decomposition of work and heat currents into local and non-local components. We find that the non-local heat current, as well as both the local and non-local work currents, are linked to the system quantum coherence. We provide explicit expressions of coherence-related quantities that determine the work currents under various intrasystem interactions. Our scheme is versatile, capable of functioning as a refrigerator, an engine, and an accelerator, with its performance being highly sensitive to the configuration settings. These findings establish a connection between thermodynamic quantities and quantum coherence, supplying valuable insights for the design of quantum thermal machines.
Abstract The characterization and control of quantum effects in the performance of thermodynamic tasks may open new avenues for small thermal machines working in the nanoscale. We study the impact of coherence in the energy basis in the operation of a small thermal machine which can act either as a heat engine or as a refrigerator. We show that input coherence may enhance the machine performance and allow it to operate in otherwise forbidden regimes. Moreover, our results also indicate that, in some cases, coherence may also be detrimental, rendering optimization of particular models a crucial task for benefiting from coherence-induced enhancements.