Abstract
Quantum heat engines (QHE) are thermal machines where the working substance is a quantum object. In the extreme case, the working medium can be a single particle or a few-level quantum system. The study of QHE has shown a remarkable similarity with macroscopic thermodynamical results, thus raising the issue of what is quantum in quantum thermodynamics. Our main result is the thermodynamical equivalence of all engine types in the quantum regime of small action with respect to Planck’s constant. They have the same power, the same heat, and the same efficiency, and they even have the same relaxation rates and relaxation modes. Furthermore, it is shown that QHE have quantum-thermodynamic signature; i.e., thermodynamic measurements can confirm the presence of quantum effects in the device. We identify generic coherent and stochastic work extraction mechanisms and show that coherence enables power outputs that greatly exceed the power of stochastic (dephased) engines.
- Received 14 May 2015
DOI:https://doi.org/10.1103/PhysRevX.5.031044
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Published by the American Physical Society
Popular Summary
It is now possible to manipulate single atoms and ions, which enables the construction of heat engines and refrigerators whose cores are comprised of a single particle. Surprisingly, these microscopic quantum heat machines have been found to obey classical thermodynamical results, which is puzzling. It is expected that quantum effects would modify classical thermodynamics results on the atomic scale. Hence, some of the key outstanding questions in the field of quantum thermodynamic include: What is quantum about quantum heat machines? Is classical thermodynamics sufficient to explain all thermodynamic effects in single-particle heat machines? Here, we present three thermodynamics effects that have a quantum origin with no classical analog.
We examine the three main types of engines: four-stroke, two-stroke, and continuous. Our main result is that in the quantum regime of small engine action with respect to Planck’s constant, different engine types become thermodynamically equivalent. We explain this result by isolating two different work-extraction mechanisms: the coherent (quantum) mechanism and the stochastic (classical) mechanism. We theoretically show why all of the engine types have the same power, heat, and efficiency. In addition, we demonstrate that the coherent mechanism can lead to a significant power boost. To isolate the signature of this quantum boost, we derive a limit on the power of classical stochastic engines. Power above this limit is evidence of quantum coherence. Therefore, thermodynamic measurements can reveal the presence of quantum effects at work.
Our results, which can be applied to both refrigerators and engines, will hopefully motivate experimentalists to reproduce our theoretical predictions. We expect that our findings and tools will lead to the discovery of additional quantum thermodynamic effects that have no classical analogs. Such additional findings will help to formulate a more complete theory that shows how quantum agents such as entanglement, discord, quantum statistic, and interference affect thermodynamic measurements. It will be intriguing to discover what other “quantum thermodynamic signatures” can be found.
