Universal thermodynamic limit of quantum engine efficiency

Bartłomiej Gardas, Sebastian Deffner

The Carnot statement of the second law of thermodynamics poses an upper limit on the efficiency of all heat engines. Recently, it has been studied whether generic quantum features such as coherence and quantum entanglement could allow for quantum devices with efficiencies larger than the Carnot efficiency. The present study shows that this is not permitted by the laws of thermodynamics-independent of the model. We will show that rather the definition of heat has to be modified to account for the thermodynamic cost of maintaining non-Gibbsian equilibrium states. Our theoretical findings are illustrated for two experimentally relevant examples.

Hao Wang

Jong-Min Park, Sangyun Lee, Hyun-Myung Chun +1 more

The second law of thermodynamics holds that the efficiency of heat engines, classical or quantum, cannot be greater than the universal Carnot efficiency. We discover another bound for the efficiency of a quantum Otto heat engine consisting of a harmonic oscillator. Dynamics of the engine is governed by the Lindblad equation for the density matrix, which is mapped to the Fokker-Planck equation for the quasiprobability distribution. Applying stochastic thermodynamics to the Fokker-Planck equation system, we obtain the ℏ-dependent quantum mechanical bound for the efficiency. It turns out that the bound is tighter than the Carnot efficiency. The engine achieves the bound in the low-temperature limit where quantum effects dominate. Our work demonstrates that quantum nature could suppress the performance of heat engines in terms of efficiency bound, work, and power output.

Aslı Tuncer, Özgür Esat Müstecaplıoğlu

Otavio A. D. Molitor

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.