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.
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.
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 investigate the finite-time performance of a quantum endoreversible Carnot engine cycle and its inverse operation — Carnot refrigeration cycle, employing a spin-1/2 system as the working substance. The thermal machine is alternatively driven by a hot boson bath of inverse temperature β h and a cold boson bath at inverse temperature β c (>β h). While for the engine model the hot bath is constructed to be squeezed, in the refrigeration cycle the cold bath is established to be squeezed, with squeezing parameter r. We obtain the analytical expressions for both efficiency and power in heat engines and for coefficient of performance and cooling rate in refrigerators. We find that, in the high-temperature limit, the efficiency at maximum power is bounded by the analytical value η + = 1 − sech ( 2 r ) ( 1 − η C ) , and the coefficient of performance at the maximum figure of merit is limited by ε + = sech ( 2 r ) ( 1 + ε C ) sech ( 2 r ) ( 1 + ε C ) − ε C − 1 , where η C = 1 – β h/β c and ε C = β h/(β c – β h) are the respective Carnot values of the engines and refrigerators. These analytical results are identical to those obtained from the Carnot engines based on harmonic systems, indicating that the efficiency at maximum power and coefficient at maximum figure of merit are independent of the working substance.
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 consider a quantum endoreversible Carnot engine cycle and its inverse operation–Carnot refrigeration cycle, working between a hot bath of inverse temperature βh and a cold bath at inverse temperature βc. For the engine model, the hot bath is constructed to be squeezed, whereas for the refrigeration cycle, the cold bath is set to be squeezed. In the high-temperature limit, we analyze efficiency at maximum power and coefficient of performance at maximum figure of merit, revealing the effects of the times allocated to two thermal-contact and two adiabatic processes on the machine performance. We show that, when the total time spent along the two adiabatic processes is negligible, the efficiency at maximum power reaches its upper bound, which can be analytically expressed in terms of squeezing parameter r: ηana∗=1−sech[2r]1−ηC, with the Carnot efficiency ηC=1−βh/βc and the coefficient of performance at maximum figure of merit is bounded from the upper side by the analytical function: εana∗=1+εCsech[2r](1+εC)−εC−1, where εC=βh/(βc−βh).
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 Recent theoretical and experimental studies in quantum heat engines show that, in the quasi-static regime, it is possible to have higher efficiency than the limit imposed by Carnot, provided that engineered reservoirs are used. The quasi-static regime, however, is a strong limitation to the operation of heat engines, since an infinitely long time is required to complete a cycle. In this paper we propose a two-level model as the working substance to perform a quantum Otto heat engine surrounded by a cold thermal reservoir and a squeezed hot thermal reservoir. Taking advantage of this model we show a striking achievement, that is to attain unity efficiency even at non-null power.