Łobejko Marcin
Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308, Gdańsk, Poland.
Nat Commun. 2021 Feb 10;12(1):918. doi: 10.1038/s41467-021-21140-4.
In classical thermodynamics, the optimal work is given by the free energy difference, what according to the result of Skrzypczyk et al. can be generalized for individual quantum systems. The saturation of this bound, however, requires an infinite bath and ideal energy storage that is able to extract work from coherences. Here we present the tight Second Law inequality, defined in terms of the ergotropy (rather than free energy), that incorporates both of those important microscopic effects - the locked energy in coherences and the locked energy due to the finite-size bath. The former is solely quantified by the so-called control-marginal state, whereas the latter is given by the free energy difference between the global passive state and the equilibrium state. Furthermore, we discuss the thermodynamic limit where the finite-size bath correction vanishes, and the locked energy in coherences takes the form of the entropy difference. We supplement our results by numerical simulations for the heat bath given by the collection of qubits and the Gaussian model of the work reservoir.
在经典热力学中，最优功由自由能差给出，根据斯克里普奇克等人的结果，这可以推广到单个量子系统。然而，这个界限的饱和需要一个无限大的热库和能够从相干性中提取功的理想能量存储。在这里，我们提出了一个严格的第二定律不等式，它是根据能质（而不是自由能）定义的，该不等式包含了这两个重要的微观效应——相干性中的锁定能量和由于有限尺寸热库导致的锁定能量。前者仅由所谓的控制边缘态来量化，而后者由全局被动态和平衡态之间的自由能差给出。此外，我们讨论了有限尺寸热库修正消失且相干性中的锁定能量呈现熵差形式的热力学极限情况。我们通过对由量子比特集合给出的热库和功库的高斯模型进行数值模拟来补充我们的结果。
