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arXiv:2204.04782 · Physical review. E

Optimization of asymmetric quantum Otto engine cycles

Rahul Shastri, B. Prasanna Venkatesh

Published Aug 23, 2022• 12 citations
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Abstract

We consider the optimization of the work output and fluctuations of a finite-time quantum Otto heat engine cycle consisting of compression and expansion work strokes of unequal duration. The asymmetry of the cycle is characterized by a parameter r_{u} giving the ratio of the times for the compression and expansion work strokes. For such an asymmetric quantum Otto engine cycle, with working substance chosen as a harmonic oscillator or a two-level system, we find that the optimal values of r_{u} maximizing the work output and the reliability (defined as the ratio of average work output to its standard deviation) shows discontinuities as a function of the total time taken for the cycle. Moreover we identify cycles of some specific duration where both the work output and the reliability take their largest values for the same value of the asymmetry parameter r_{u}.

DOI
10.1103/physreve.106.024123

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We consider the optimization of the work output and fluctuations of a finite-time quantum Otto heat engine cycle consisting of compression and expansion work strokes of unequal duration. The asymmetry of the cycle is characterized by a parameter r_{u} giving the ratio of the times for the compression and expansion work strokes. For such an asymmetric quantum Otto engine cycle, with working substance chosen as a harmonic oscillator or a two-level system, we find that the optimal values of r_{u} maximizing the work output and the reliability (defined as the ratio of average work output to its standard deviation) shows discontinuities as a function of the total time taken for the cycle. Moreover we identify cycles of some specific duration where both the work output and the reliability take their largest values for the same value of the asymmetry parameter r_{u}.
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.
We present a detailed study of an asymmetrically driven quantum Otto engine with a time-dependent harmonic oscillator as its working medium. We obtain analytic expressions for the upper bounds on the efficiency of the engine for two different driving schemes having asymmetry in the expansion and compression work strokes. We show that the Otto cycle under consideration cannot operate as a heat engine in the low-temperature regime. Then, we show that the friction in the expansion stroke is significantly more detrimental to the performance of the engine as compared to the friction in the compression stroke. Further, by comparing the performance of the engine with sudden expansion, sudden compression, and both sudden strokes, we uncover a pattern of connections between the operational points, and we indicate the optimal operation regime for each case. Finally, we analytically characterize the complete phase diagram of the Otto cycle for both driving schemes and highlight the different operational modes of the cycle as a heat engine, refrigerator, accelerator, and heater.
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.
Abstract We study a quantum harmonic Otto engine under a hot squeezed thermal reservoir with asymmetry between the two adiabatic branches introduced by considering different speeds of the driving protocols. In the first configuration, the driving protocol for the expansion stroke is sudden-switch in nature and compression stroke is driven adiabatically, while the second configuration deals with the converse situation. In both cases, we obtain analytic expressions for the upper bound on efficiency and efficiency at optimal work output, which reveals a significant difference between the two configurations. Additionally, we find that the maximum achievable efficiency in sudden expansion case is 1/2 only while it approaches unity for the sudden compression stroke. Further, we study the effect of increasing degree of squeezing on the efficiency and work output of the engine and indicate the optimal operational regime for both configurations under consideration. Finally, by studying the full phase-diagram of the Otto cycle we observe that the operational region of the engine mode grows with increasing squeezing at the expense of refrigeration regime.
Abstract We consider a quantum endoreversible Otto engine cycle and its inverse operation-Otto refrigeration cycle, employing two-level systems as the working substance and operating in dual-squeezed reservoirs. We demonstrate that the efficiency of heat engines at maximum work output and the coefficient of performance for refrigerators at the maximum χ criterion will degenerate to η − = η C/(2 – η C) and ε − = ( 9 + 8 ε C − 3 ) / 2 when symmetric squeezing is satisfied, respectively. We also investigated the influences of squeezing degree on the performance optimization of quantum Otto heat engines at the maximum work output and refrigerators at the maximum χ criterion. These analytical results show that the efficiency of heat engines at maximum work output and the coefficient of performance for refrigerators at the maximum χ criterion can be improved, reduced or even inhibited in asymmetric squeezing. Furthermore, we also find that the efficiency of quantum Otto heat engines at maximum work output is lower than that obtained from the Otto heat engines based on a single harmonic oscillator system. However, the coefficient of performance of the corresponding refrigerator is higher.
We study a quantum Otto cycle in which the strokes are performed in finite time. The cycle involves energy measurements at the end of each stroke to allow for the respective determination of work. We then optimize for the work and efficiency of the cycle by varying the time spent in the different strokes and find that the optimal value of the ratio of time spent on each stroke goes through sudden changes as the parameters of this cycle vary continuously. The position of these discontinuities depends on the optimized quantity under consideration such as the net work output or the efficiency.