在Alicki的开创性工作[J. Phys. A 12，L103（1979）]中，引入了由具有随时间变化的驱动场的耗散主方程控制的量子系统的热和功。Alicki的工作是在薛定谔的图片;在这里，我们将这些定义扩展到海森堡和相互作用的图片。我们表明，为了避免一致性问题，在热通量和功率（功通量）的定义的全时间导数应取代偏时间导数。我们还提出了另一种方法来划分的能量通量，这不同于Alicki的瞬时相互作用能与外部场不包括直接。然后，我们继续推广Alicki的定义的权力取代原来的系统和外部驱动场与一个更大的，二分系统，由时间无关的哈密顿量。利用热通量的定义和功率的广义定义，我们导出了完全二分系统和部分示踪子系统的热力学热力学第一定律的微分形式。虽然第二定律（克劳修斯制定）是满足完整的二分系统，我们发现，在一般情况下，没有严格的制定第二定律的部分跟踪子系统，除非某些额外的要求得到满足。然而，一旦这些要求得到满足，第二定律的卡诺公式和克劳修斯公式都得到满足。我们说明这两个简单的Jaynes-Cummings模型（JCM）和扩展的耗散Jaynes-Cummings模型（ED-JCM），这是一个量子放大器的模型的热力学分析。
英文摘要：
Heat and work for quantum systems governed by dissipative master equations with a time-dependent driving field were introduced in the pioneering work of Alicki [J. Phys. A 12, L103 (1979)]. Alicki's work was in the Schroedinger picture; here we extend these definitions to the Heisenberg and interaction pictures. We show that in order to avoid consistency problems, the full time derivatives in the definitions for heat flux and power (work flux) should be replaced by partial time derivatives. We also present an alternative approach to the partitioning of the energy flux which differs from that of Alicki in that the instantaneous interaction energy with the external field is not included directly. We then proceed to generalize Alicki's definition of power by replacing the original system and its external driving field with a larger, bipartite system, governed by a time-independent Hamiltonian. Using the definition of heat flux and the generalized definition of power, we derive the first law of thermodynamics in differential form, both for the full bipartite system and the partially traced subsystems. Although the second law (Clausius formulation) is satisfied for the full bipartite system, we find that in general there is no rigorous formulation of the second law for the partially traced subsystem unless certain additional requirements are met. Once these requirements are satisfied, however, both the Carnot and the Clausius formulations of the second law are satisfied. We illustrate this thermodynamic analysis on both the simple Jaynes-Cummings model (JCM) and an extended dissipative Jaynes-Cummings model (ED-JCM), which is a model for a quantum amplifier.
Quantum speed limit time for bipartite entanglement in neutrino oscillations in matter with nonstandard interactions
Indian Institute of Science, Bangalore（印度科学学院）；SVKM’s Narsee Monjee Institute of Management Studies (NMIMS) Deemed-to-be-University（SVKM纳尔西·蒙吉管理研究所（NMIMS））；Indian Institute of Technology Jodhpur（焦特普尔印度理工学院）；University of Hyderabad（海德拉巴大学）
