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Quantum Science and Technology

Optimization of energy production in two-qubit heat engines using the ecological function

J J Fernández

Published Apr 2, 2022• 15 citations
Publisher

Abstract

Abstract We study the ecological regime of quantum heat engines where the heat transfer between the environment and the engine is mediated with two qubits that act as energy filters and allow the conversion of heat into work. Using quantum thermodynamics, the theory of open quantum system and the fundamentals of finite-time thermodynamics we obtain the output power, the ecological function and the entropy production of the engine. Then, we optimize the functioning to the ecological function to find the range of efficiencies for which the system works optimally under the ecological criterium. We find that (i) the maximum value of the ecological function depends on the thermal copulings and the energies of the qubits that define the engine. (ii) We can define an ecological working region where the engine works producing a power that is similar to the maximum power but where it rejects much less heat to the environment. (iii) That the range of efficiencies defining the ecological region depends on the parameters defining the engine.(iv) An optimal working region where both the power and the ecological function are big is defined for each machine.

DOI
10.1088/2058-9565/ac635a

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Abstract We study the ecological regime of quantum heat engines where the heat transfer between the environment and the engine is mediated with two qubits that act as energy filters and allow the conversion of heat into work. Using quantum thermodynamics, the theory of open quantum system and the fundamentals of finite-time thermodynamics we obtain the output power, the ecological function and the entropy production of the engine. Then, we optimize the functioning to the ecological function to find the range of efficiencies for which the system works optimally under the ecological criterium. We find that (i) the maximum value of the ecological function depends on the thermal copulings and the energies of the qubits that define the engine. (ii) We can define an ecological working region where the engine works producing a power that is similar to the maximum power but where it rejects much less heat to the environment. (iii) That the range of efficiencies defining the ecological region depends on the parameters defining the engine.(iv) An optimal working region where both the power and the ecological function are big is defined for each machine.
The purpose of this paper is to present a study of finite-time thermodynamics applied to evaluate the ecological performance of a quantum heat engine which operates between two thermal reservoirs using the working substance of spin-1/2 systems. The quantum heat engine cycle is composed of two isothermal processes, an adiabatic process and an isomagnetic field process. A sequence of time evolution was determined from the quantum angular momentum rate based on the semigroup approach and the quantum master equation. The individual time duration is added to account for the total cycle time. The objective ecological function representing a compromise between power output and irreversibility is maximized with respect to cycle temperature ratio. Effects of thermal reservoir temperature ratio and magnetic field ratio on the ecological function have been discussed. A comparison of quantum heat engine performance under maximum ecological function and maximum power conditions is also presented.
Abstract We present the quantum Otto machine under different optimization criterion when function either as a heat engine or a refrigerator. We examine the optimal performance of the heat engine and refrigerator depending on their efficiency, output power and maximum entropy production. For heat engine case, we obtain the expression for the upper and lower bounds efficiencies at maximum power and maximum ecological function. The optimal ecological performance is laying between the maximum efficiency and the maximum power output. On the other hand, the quantum Otto refrigerator coefficient of performance is optimized for three different criterion – cooling power, χ criterion(product of performance and power) and ecological function. We further study the dimen-sionless power loss to the cold reservoir when the machine is operating as a heat engine as well as its counterpart for the refrigerator case. We find that the maximum operation of the heat engine (refrigerator) cycle is when optimized with respect to hot (cold) reservoir frequency.
Abstract We optimize one-qubit Novikov quantum heat engines with a dissipative heat leak using the formalisms of open-system Quantum Mechanics and the Finite-Time Thermodynamics. We show that the leak changes the power-efficiency and the efficient-power-efficiency curves, reduces the maximum efficiency of the machine and does not change its power. We also discuss the effects of the leak on the power that is rejected from the machine to the environment. Finally, we study the high-temperature limit to check that the engine reduces in this limit to a classic Novikov heat engine.
A model of a quantum heat engine with heat resistance, internal irreversibility and heat leakage and many non-interacting spin-1/2 systems is established in this paper. The quantum heat engine cycle is composed of two isothermal processes and two irreversible adiabatic processes and is referred to as a spin quantum Carnot heat engine. Based on the quantum master equation and the semi-group approach, equations of some important performance parameters, such as power output, efficiency, entropy generation rate and ecological function (a criterion representing the optimal compromise between exergy output rate and exergy loss rate), for the irreversible spin quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. The effects of internal irreversibility and heat leakage on ecological performance are discussed in detail.
We present a detailed study of a three-level quantum heat engine operating at maximum efficient power function, a trade-off objective function defined by the product of the efficiency and power output of the engine.The efficient power function represents a trade-off between the power output and efficiency of a heat engine.Engines working in the maximum efficient power regime operate at finite power, with finite efficiency lying in between the regimes of maximum power and maximum efficiency (Carnot efficiency).First, for near-equilibrium conditions, we find a general expression for the efficiency and establish the universal nature of efficiency at maximum power and maximum efficient power.Then in the high-temperature limit, optimizing with respect to one parameter while constraining the other one, we obtain the lower and upper bounds on the efficiency for both strong as well as weak matter-field coupling conditions.Except for the weak matter-field coupling condition, the obtained bounds on the efficiency exactly match with the bounds already known for some models of classical heat engines.Further for weak matter-field coupling, we derive some new bounds on the efficiency of the engine which lie beyond the range covered by bounds obtained for strong matter-field coupling.We conclude by comparing the performance of our three-level quantum heat engine in maximum power and maximum efficient power regimes and show that the engine operating at maximum efficient power produces at least 88.89% of the maximum power output while considerably reducing the power loss due to entropy production.Finally, to complete our analysis, we review the experimental setup of a recently realized effective three-level quantum engine.