Quantum Carnot cycle with inner friction
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Quantum Carnot cycle with inner friction Selçuk Çakmak1
· Ferdi Altintas2
Received: 18 March 2020 / Accepted: 4 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract A single driven spin is investigated as the working substance of a six-stroke irreversible quantum Carnot cycle. The role of inner friction associated with the finite-time adiabatic transformations on the cycle efficiency and the harvested work are investigated in detail. The inner friction is found to significantly reduce the work output and the cycle efficiency which can make the engine incapable to produce positive work for the too fast adiabatic transformations. The ideal Carnot efficiency is found to be reached only for the quasistatic transformations. A deviation of the cycle efficiency from the classical Carnot efficiency has been given by an efficiency lag which is directly related to the total entropy production due to the inner friction. The released heat in the relaxation processes of the cycle is associated with the entropy production and the inner friction. The extension of the results for a scale-invariant quantum working substance and the possible experimental implementation of the irreversible quantum Carnot cycle in a liquid-state nuclear magnetic resonance setup are also discussed. Keywords Quantum thermodynamics · Quantum heat engine · Quantum Carnot cycle · Inner friction · Nuclear magnetic resonance
1 Introduction Since the recognition of a three-level maser as a heat engine operating at the Carnot limit [1], the concepts of quantum thermodynamic processes and quantum heat engines have been studied extensively [2–55]. A quantum system as a working medium extracts useful work by operating between a source bath and an entropy sink through a quantum generalization of the classical thermodynamic cycle [2–4]. Recently, different exper-
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Selçuk Çakmak [email protected] Ferdi Altintas [email protected]
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Department of Software Engineering, University of Samsun, 55420 Samsun, Turkey
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Department of Physics, Bolu Abant Izzet Baysal University, 14280 Bolu, Turkey 0123456789().: V,-vol
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imentally feasible quantum systems are proposed to be engineered as a nanoscale thermal engine [5–12]. Moreover, quantum heat engines are implemented experimentally in several setups [13–17]. Both quantum and thermal fluctuations are relevant for the heat engines at nanoscale. The quantum features of the working substance and the reservoirs make the nanoscale engine to exhibit several unusual features. For instance, a quantum heat engine fueled by the coherent resources can harvest useful work even more efficient than the classical Carnot engine [18–23]. On the other hand, modifying the thermodynamic definitions to account for the cost of maintaining the non-equilibrium states has shown to hold the Carnot statement for the quantum heat engines [45,46]. References [24–26] show that the internal quantum coherence is responsible for the nanoscale engine
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