Construction of a quantum Carnot heat engine cycle
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Construction of a quantum Carnot heat engine cycle Selçuk Çakmak1
· Mustafa Çandır2 · Ferdi Altintas2
Received: 26 April 2020 / Accepted: 18 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The microscopic state description of an irreversible quantum Carnot cycle for a general quantum working medium is investigated. An efficiency lag term, which quantifies the deviation of the irreversible cycle efficiency from the classical Carnot efficiency, is given in terms of the total entropy increase in the universe. The efficiency lag and the total entropy increase in the universe are directly connected to the quantum relative entropy between the density matrices obtained at the end of the quantum adiabatic and the relaxation steps of the cycle. The total entropy increase and the efficiency lag are found to be always nonnegative quantities. Our results give a direct proof that the irreversible cycle efficiency is always smaller than the classical Carnot efficiency. Two interacting spins under an external magnetic field are proposed as the working medium of the irreversible quantum Carnot cycle. The external magnetic field is considered to be quasistatically changed during the steps of the cycle. The coupling between the spins is found to break down the scale invariance and make the quantum Carnot cycle irreversible. It is shown that while the quantum coupling can lower the cycle efficiency monotonically to zero, it can make the irreversible cycle to produce more work than the one obtained from the uncoupled spins. The conditions in which one can always construct a reversible Carnot cycle for the coupled spin working medium are also given. Keywords Quantum thermodynamics · Quantum heat engine · Quantum Carnot cycle · Non-equilibrium thermodynamics · Irreversible cycle
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Selçuk Çakmak [email protected] Mustafa Çandır [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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1 Introduction Thermodynamics of the systems at the nanoscale have been devoted a lot of attention, recently [1–66]. The extension of the classical thermodynamic processes and the thermal machine cycles to the quantum domain have been, therefore, become an active research field [1–3]. Three-level maser has been introduced as a kind of a quantum heat engine a long time ago which can operate at the classical Carnot efficiency [4]. Since then, numerous stimulating proposals [5–12] and experimental realizations [13–18] of the nanoscale thermal machines have been given. A quantum heat engine performs a quantum mechanical version of a thermodynamic cycle by employing a quantum system as a working substance. Both thermal and quantum fluctuations affect the operation of the quantum heat engines. The main objective in the study of the quantum heat engines is to use the quantum
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