We demonstrate the existence of universal features in the finite-time thermodynamics of quantum machines by considering a many-body quantum Otto cycle in which the working medium is driven across quantum critical points during the unitary strokes.Specifically, we consider a quantum engine powered by dissipative energizing and relaxing baths.We show that under very generic conditions, the output work is governed by the Kibble-Zurek mechanism; i.e., it exhibits a universal power-law scaling with the driving speed through the critical points.We also optimize the finite-time thermodynamics as a function of the driving speed.The maximum power and the corresponding efficiency take a universal form, and are reached for an optimal speed that is governed by the critical exponents.We exemplify our results by considering a transverse-field Ising spin chain as the working medium.For this model, we also show how the efficiency and power vary as the engine becomes critical.
We demonstrate the existence of universal features in the finite-time thermodynamics of quantum machines by considering a many-body quantum Otto cycle in which the working medium is driven across quantum critical points during the unitary strokes.Specifically, we consider a quantum engine powered by dissipative energizing and relaxing baths.We show that under very generic conditions, the output work is governed by the Kibble-Zurek mechanism; i.e., it exhibits a universal power-law scaling with the driving speed through the critical points.We also optimize the finite-time thermodynamics as a function of the driving speed.The maximum power and the corresponding efficiency take a universal form, and are reached for an optimal speed that is governed by the critical exponents.We exemplify our results by considering a transverse-field Ising spin chain as the working medium.For this model, we also show how the efficiency and power vary as the engine becomes critical.
Driving a quantum system across quantum critical points leads to non-adiabatic excitations in the system. This in turn may adversely affect the functioning of a quantum machine which uses a quantum critical substance as its working medium. Here we propose a bath-engineered quantum engine (BEQE), in which we use the Kibble–Zurek mechanism and critical scaling laws to formulate a protocol for enhancing the performance of finite-time quantum engines operating close to quantum phase transitions. In the case of free fermionic systems, BEQE enables finite-time engines to outperform engines operating in the presence of shortcuts to adiabaticity, and even infinite-time engines under suitable conditions, thus showing the remarkable advantages offered by this technique. Open questions remain regarding the use of BEQE based on non-integrable models.
We study finite-time driving across second-order dissipative quantum phase transitions described by Lindblad dynamics. We show that the nonadiabatic entropy production, which quantifies deviations from the instantaneous nonequilibrium steady state, exhibits universal power-law scaling with the ramp duration in analogy to the Kibble-Zurek mechanism for closed systems. This establishes the universality of irreversible dissipation induced by driving an open quantum system near criticality. Furthermore, in systems described by bosonic Gaussian states, our scaling laws predict that the nonadiabatic entropy production is independent of driving speed to leading order, revealing a distinctive feature of Gaussian dissipative quantum phase transitions. We validate these analytical predictions in the thermodynamic limit of the driven-dissipative Dicke model and via finite-size scaling in the open Kerr model. Our results establish a general framework for understanding universal nonequilibrium response and thermodynamic irreversibility in critical open quantum systems.
We investigate a finite-time quantum Otto engine within the framework of gauge-invariant quantum thermodynamics, using the Lipkin-Meshkov-Glick model as the working medium. In this formulation, thermodynamic quantities are defined on equivalence classes of thermodynamically indistinguishable states, leading naturally to gauge-invariant notions of work, heat, entropy, and efficiency. We derive explicit expressions for these quantities and show that the usual work performed during the unitary strokes decomposes into an invariant contribution, associated with changes in the instantaneous energy spectrum and populations, and a coherent contribution arising from finite-time quantum coherences. This decomposition induces the corresponding splittings of engine efficiency and entropy production, providing a geometric interpretation of finite-time irreversibility and clarifying the role of coherence in work extraction. By analyzing the cycle's dependence on driving speed and system size, we identify the engine's operating region and investigate the influence of criticality. We show that crossing the critical region substantially reduces the parameter space in which the cycle operates as a heat engine. At the same time, whenever the engine condition remains satisfied, the discrepancy between the conventional and gauge-invariant descriptions becomes strongly suppressed, indicating that the gauge-invariant sector predominantly carries the extracted work. These results establish a direct connection between gauge-invariant thermodynamics, finite-time irreversibility, and work extraction in many-body quantum thermal machines.
In the last decade, the study of thermodynamic phenomena in ultra-small scales, where quantum mechanics becomes imperative, has gained a lot of attention. The possibility of controlling single quantum states in nowadays experimental setups has encouraged a more intense inquiry over the intersection between thermodynamics and quantum mechanics, which is known as quantum thermodynamics. Particularly relevant in this framework is the study of quantum heat engines, that is, quantum systems undergoing thermodynamic cycles. Thermodynamic cycles contain all the aspects of thermodynamics, thus its a good testbed for a better comprehension of the thermodynamics of quantum systems. Moreover, modelling quantum heat engines is crucial for the design of future ultra-small engines. Nonetheless, another aspect must be taken into account, finite-time operation. Its very important for the optimization of the output power of the engine. In this dissertation, we present a new model of finite-time quantum heat engines. By making use of collisional models, we construct a model in which a generic quantum chain experiences sequential pure heat and pure work strokes. Dictated by stroboscopic evolution, the engines state goes through a transient regime until the limit-cycle is reached. After the achievement of the limit-cycle, our results indicate that only the boundary sites of the quantum chain are relevant for the heat currents exchanged with the baths. By means of analytical and numerical methods, we present how the model is useful for optimizing the output power of stroke-based quantum heat engines, without decreasing their respective efficiencies. Lastly, we prove that there is a universal efficiency value, the Otto efficiency, for a whole family of models containing a specific kind of internal interactions. For completeness, other methods from the literature which deal with finite-time quantum heat engines are also presented and discussed.
We study the optimization of the performance of arbitrary periodically driven thermal machines. Within the assumption of fast modulation of the driving parameters, we derive the optimal cycle that universally maximizes the extracted power of heat engines, the cooling power of refrigerators, and in general any linear combination of the heat currents. We denote this optimal solution as ``generalized Otto cycle'' since it shares the basic structure with the standard Otto cycle, but it is characterized by a greater number of fast strokes. We bound this number in terms of the dimension of the Hilbert space of the system used as working fluid. The generality of these results allows for a widespread range of applications, such as reducing the computational complexity for numerical approaches, or obtaining the explicit form of the optimal protocols when the system-baths interactions are characterized by a single thermalization scale. In this case, we compare the thermodynamic performance of a collection of optimally driven noninteracting and interacting qubits. Remarkably, for refrigerators the noninteracting qubits perform almost as well as the interacting ones, while in the heat engine case there is a many-body advantage both in the maximum power, and in the efficiency at maximum power. Additionally, we illustrate our general results studying the paradigmatic model of a qutrit-based heat engine. Our results strictly hold in the semiclassical case in which no coherence is generated by the driving, and finally we discuss the noncommuting case.
We consider a generic four-stroke quantum Otto engine consisting of two unitary and two thermalization strokes with an arbitrary many-body working medium. Using the Schwinger-Keldysh nonequilibrium Green's function formalism, we provide an analytical expression for the cumulant generating function corresponding to the joint probability distribution of nonequilibrium work and heat. The obtained result is valid up to the second order of the external driving amplitude. We then focus on the linear response limit and obtained Onsager's transport coefficients for the generic Otto cycle and show that the traditional fluctuation-dissipation relation for the total work is violated in the quantum domain, whereas for heat it is preserved. This leads to remarkable consequences in obtaining universal constraints on heat and work fluctuations for engine and refrigerator regimes of the Otto cycle and further allows us to make connections to the thermodynamic uncertainty relations. These findings are illustrated using a paradigmatic model that can be feasibly implemented in experiments.