We establish a finite-time external field-driven quantum tricycle model. Within the framework of slow driving perturbation, the perturbation expansion of heat in powers of time can be derived during the heat exchange processes. Employing the method of Lagrange multiplier, we optimize the cooling performance of the tricycle by considering the cooling rate and the figure of merit, which is the product of the coefficient of performance and cooling rate, as objective functions. Our findings reveal the optimal operating region of the tricycle, shedding light on its efficient performance.
We establish a finite-time external field-driven quantum tricycle model. Within the framework of slow driving perturbation, the perturbation expansion of heat in powers of time can be derived during the heat exchange processes. Employing the method of Lagrange multiplier, we optimize the cooling performance of the tricycle by considering the cooling rate and the figure of merit, which is the product of the coefficient of performance and cooling rate, as objective functions. Our findings reveal the optimal operating region of the tricycle, shedding light on its efficient performance.
We establish a finite-time quantum tricycle driven by an external field and investigate its thermodynamic performance in the slow-driving regime. By developing a perturbative expansion of heat with respect to operation time, we capture the dynamics of heat exchange processes beyond the quasistatic limit. Within a geometric framework, we derive fundamental bounds on trade-offs between the cooling rate, coefficient of performance, and dissipation, governed by the thermodynamic length and trajectory geometry in control space. Our findings unveil intrinsic limits to the performance of quantum thermal machines and highlight the role of geometry in shaping finite-time thermodynamics. This work advances the fundamental understanding of quantum thermodynamic processes and offers guiding principles for the design of next-generation quantum technologies.
The Drazin inverse of the Liouvillian superoperator provides a solution to determine the dynamics of a time-dependent system governed by the Markovian master equation. Under the condition of slow driving, the perturbation expansion of the density operator of the system in powers of time can be derived. As an application, a finite-time cycle model of the quantum refrigerator driven by a time-dependent external field is established. The method of the Lagrange multiplier is adopted as a strategy to find the optimal cooling performance. The figure of merit given by the product of the coefficient of performance and the cooling rate is taken as a new objective function, and, consequently, the optimally operating state of the refrigerator is revealed. The effects of the frequency exponent determining dissipation characteristics on the optimal performance of the refrigerator are discussed systemically. The results obtained show that the adjacent areas of the state of the maximum figure of merit are the best operation region of low-dissipative quantum refrigerators.
Quantum thermodynamics supplies a consistent description of quantum heat engines and refrigerators up to a single few-level system coupled to the environment. Once the environment is split into three (a hot, cold, and work reservoir), a heat engine can operate. The device converts the positive gain into power, with the gain obtained from population inversion between the components of the device. Reversing the operation transforms the device into a quantum refrigerator. The quantum tricycle, a device connected by three external leads to three heat reservoirs, is used as a template for engines and refrigerators. The equation of motion for the heat currents and power can be derived from first principles. Only a global description of the coupling of the device to the reservoirs is consistent with the first and second laws of thermodynamics. Optimization of the devices leads to a balanced set of parameters in which the couplings to the three reservoirs are of the same order and the external driving field is in resonance. When analyzing refrigerators, one needs to devote special attention to a dynamical version of the third law of thermodynamics. Bounds on the rate of cooling when Tc→0 are obtained by optimizing the cooling current. All refrigerators as Tc→0 show universal behavior. The dynamical version of the third law imposes restrictions on the scaling as Tc→0 of the relaxation rate γc and heat capacity cV of the cold bath.
In this work we considered the quantum Otto cycle within an optimization framework. The goal was maximizing the power for a heat engine or maximizing the cooling power for a refrigerator. In the field of finite-time quantum thermodynamics it is common to consider frictionless trajectories since these have been shown to maximize the work extraction during the adiabatic processes. Furthermore, for frictionless cycles, the energy of the system decouples from the other degrees of freedom, thereby simplifying the mathematical treatment. Instead, we considered general limit cycles and we used analytical techniques to compute the derivative of the work production over the whole cycle with respect to the time allocated for each of the adiabatic processes. By doing so, we were able to directly show that the frictionless cycle maximizes the work production, implying that the optimal power production must necessarily allow for some friction generation so that the duration of the cycle is reduced.
The study of nanoscopic thermal devices attracts an increasing attention, not only because of their key role in understanding the emergence of thermodynamics from quantum theory, but also for the potential use of quantum-mechanical thermal cycles, especially refrigerators, in quantum technologies. This thesis, is devoted to the performance optimization of autonomous (heat-driven) refrigerators. For a quantum refrigerator, one has a full microscopic description of the simple system serving as a working medium, and of its interaction with the external heat baths. This enables a consistent `finite-time? thermodynamic analysis, not relying on any phenomenological assumptions about the leading sources of irreversibility, and allows to establish arguably general performance bounds, essential to benchmark the operation of realistic devices. In particular, tight and model-independent upper bounds for the coefficient of performance at maximum power, are derived here for a class of strongly coupled refrigerators, and seen to hold more generally for other types of heat and power-driven cycles. Remarkably, these ultimate limitations only depend on the particulars of the system-baths interaction at the interface with the object to be cooled. Strategies might be then defined so as to saturate those limits: It is shown how the working medium of the refrigerator may be, for instance, scaled up into a parallel multi-stage configuration, resembling that of macroscopic multi-effect absorption chillers, as a means to increase its cooling power. Similarly, by applying reservoir engineering techniques on selected transitions between the energy states of the working medium, one can mimic exploitable non-equilibrium fluctuations in the baths, capable of boosting the overall power and COP beyond what would be otherwise allowed by the second law of thermodynamics. In this way, heat-driven chillers could be set to compete on a equal footing with the best power-driven refrigerators.
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.