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arXiv:2112.10669 · Physical review. E

Unified trade-off optimization of quantum harmonic Otto engine and refrigerator

Varinder Singh, Satnam Singh, Obinna Abah, Özgür Esat Müstecaplıoğlu

Published Aug 31, 2022• 27 citations
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Abstract

We investigate quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator operating under the conditions of maximum Ω function, a trade-off objective function which represents a compromise between energy benefits and losses for a specific job, for both adiabatic and nonadiabatic (sudden) frequency modulations. We derive analytical expressions for the efficiency and coefficient of performance of the Otto cycle. For the case of adiabatic driving, we point out that in the low-temperature regime, the harmonic Otto engine (refrigerator) can be mapped to Feynman's ratchet and pawl model which is a steady-state classical heat engine. For the sudden switch of frequencies, we obtain loop-like behavior of the efficiency-work curve, which is characteristic of irreversible heat engines. Finally, we discuss the behavior of cooling power at maximum Ω function.

DOI
10.1103/physreve.106.024137

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We investigate quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator operating under the conditions of maximum Ω function, a trade-off objective function which represents a compromise between energy benefits and losses for a specific job, for both adiabatic and nonadiabatic (sudden) frequency modulations. We derive analytical expressions for the efficiency and coefficient of performance of the Otto cycle. For the case of adiabatic driving, we point out that in the low-temperature regime, the harmonic Otto engine (refrigerator) can be mapped to Feynman's ratchet and pawl model which is a steady-state classical heat engine. For the sudden switch of frequencies, we obtain loop-like behavior of the efficiency-work curve, which is characteristic of irreversible heat engines. Finally, we discuss the behavior of cooling power at maximum Ω function.
Abstract We investigate the optimal performance of the quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator under a trade-off figure of merit for both adiabatic and nonadiabatic (sudden-switch) frequency modulations. For heat engines (refrigerators), the chosen trade-off figure of merit is an objective function defined by the product of efficiency (coefficient of performance) and work output (cooling load), thus representing a compromise between them. We obtain analytical expressions for the efficiency and coefficient of performance of the harmonic Otto cycle for the optimal performance of the thermal machine in various operational regimes. Particularly, in the sudden-switch regime, we discuss the implications of the nonadiabatic driving on the performance of the thermal machine under consideration and obtain analytic expressions for the maximum achievable efficiency and coefficient of performance of the harmonic Otto thermal machine. Particularly, we show that the quantum harmonic Otto cycle driven by sudden-switch protocol cannot work as a heat engine or refrigerator in the low-temperature limit. Finally, we show that in the high-temperature limit, the frictional effects give rise to a richer structure of the phase diagram of the harmonic Otto cycle. We identify the parametric regime for the operation of the Otto cycle as a heat engine, refrigerator, accelerator, and heater.
We consider a quantum Otto refrigerator cycle of a time-dependent harmonic oscillator. We investigate the coefficient of performance at maximum figure of merit for adiabatic and nonadiabatic frequency modulations. We obtain analytical expressions for the optimal performance both in the high-temperature (classical) regime and in the low-temperature (quantum) limit. We moreover analyze the breakdown of the cooling cycle for strongly nonadiabatic driving protocols and derive analytical estimates for the minimal driving time allowed for cooling.
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.
We analyze the performance of a quantum Otto cycle, employing a time-dependent harmonic oscillator as the working fluid undergoing sudden expansion and compression strokes during the adiabatic stages, coupled to a squeezed reservoir. First, we show that the maximum efficiency that our engine can achieve is 1/2 only, which is in contrast with earlier studies claiming unit efficiency under the effect of a squeezed reservoir. Then, in the high-temperature limit, we obtain analytic expressions for the upper bound on the efficiency as well as on the coefficient of performance of the Otto cycle. The obtained bounds are independent of the parameters of the system and depend on the reservoir parameters only. Additionally, with a hot squeezed thermal bath, we obtain an analytic expression for the efficiency at maximum work which satisfies the derived upper bound. Further, in the presence of squeezing in the cold reservoir, we specify an operational regime for the Otto refrigerator otherwise forbidden in the standard case. Finally, we find the cost of creating a squeezed state from the thermal state and show that in order to harvest the benefits of squeezing, it is sufficient to squeeze only one mode of the reservoir in resonance with the transition frequency of the working fluid. Further, we show that when the cost of squeezing is included in the definition of the operational efficiency of the engine, the advantages of squeezing fade away. Still, being purely quantum mechanical fuel in nature, squeezed reservoirs are beneficial in their own way by providing us with more compact energy storage medium or offering effectively high-temperature baths without being actually too hot.
We present an analytical study of the relativistic quantum Otto cycle driven by a time-dependent harmonic oscillator. By imposing an asymmetry on the two adiabatic processes of this cycle, we obtain distinct scenarios of sudden compression and sudden expansion, and analyze how asymmetry affects the performance of the relativistic quantum Otto engine. By leveraging the Omega function as a unified performance metric, we analytically characterize the efficiency in both scenarios. Our findings demonstrate that the efficiency approaches unity in the sudden compression case, while it is restricted to one-half for the sudden expansion case. Furthermore, we investigate the impact of increasing oscillator velocity on the extracted work and identify parameter regimes where either sudden compression or sudden expansion dominates. Additionally, we examine the optimal operating point using parametric efficiency-work plots, whose loop-shaped structure shows that increasing oscillator velocity enhances both work output and efficiency. Finally, through a detailed phase diagram analysis of the Otto cycle, we observe that the operational region corresponding to the engine mode expands with increasing oscillator velocity, while the refrigeration regime shrinks correspondingly.
We study a quantum Otto engine operating with a time-dependent harmonic oscillator as its working material. We consider asymmetry between the two adiabatic processes of the Otto cycle, based on which we explore sudden expansion and sudden compression cases. We find the optimal performance of this asymmetric Otto engine under the Omega function, which represents the balance between the utilized energy and the dissipated energy of an engine. We analyze that for sudden compression stroke, the efficiency approaches unity, while it is only one-half for sudden expansion stroke. Additionally, we notice that the efficiency at the maximum Omega function consistently exceeds the maximum work efficiency in both cases. Further, we present a comparative analysis of symmetric and asymmetric Otto engines for the well-known Omega function. Then, we move our study to calculate the fractional loss of work for both the aforementioned cases. Finally, we find results for the ratio of maximum work and work under maximum Omega function. We show that the work at maximum Omega function produces 98.19\% of maximum work for both sudden compression and sudden expansion strokes.