量子轨迹随机热力学：涨落的功、热及其应用

Quantum thermodynamics is the study of thermodynamic processes of open quantum systems using quantum dynamics. It emphasizes the consistence of thermodynamic laws with quantum physics from the viewpoint of ensemble average. Although in the past decades significant progresses had been made in quantum thermodynamics, the influence of intrinsic stochastic characteristics of quantum systems on thermodynamics was not seriously investigated. It is not until very recently has this situation changed. In this proposal, based on the quantum trajectory, we attempt to establish stochastic thermodynamic theory on open quantum systems. It includes the defining of thermodynamic quantities, such as work, heat and entropy production on the quantum trajectory, the study of their mathematic and thermodynamic properties, the extensions of these results into complex quantum open systems, and the application of quantum trajectory in the research of quantum heat engines, refrigerators, and micro-devices. In addition to studying the significance of stochastic characteristics on quantum thermodynamics, our research particularly focuses on the intimate connection between thermodynamics and measurements on environment, which is also the key innovation of this proposal. The measurements do not play any role in either classical stochastic thermodynamics or conventional quantum thermodynamics, yet as the quantum trajectory is defined with respect to specific measurement on environment, this observation will be altered in stochastic quantum thermodynamics.

量子热力学致力于应用量子动力学研究开放量子系统的热力学过程。它从系综平均的观点出发，着重强调量子物理和热力学定律的自洽性。虽然量子热力学在过去的数十年里进展迅猛，但作为量子系统内禀的随机特性对热力学的影响并没有得到足够的重视。直到最近，这个局面才有了明显改变。本项目尝试以量子轨迹概念为基础，建立开放量子系统的随机热力学理论。这包括量子轨迹上的功、热、熵产生等热力学量的定义，它们的数学和热力学性质的研究，各类复杂开放系统的推广，以及量子轨迹在量子热机、制冷机和微器件研究中的应用等。除了研究随机性对量子热力学的重要意义，我们的项目也将特别关注环境测量方案和热力学理论的紧密关系，这也是本项目最突出的创新点。无论是在经典随机热力学,还是传统量子热力学中，环境测量都不扮演任何角色，但因为量子轨迹依赖于具体的环境测量，随机量子热力学将改变这一结论。

过去几十年微制备和微操控的巨大进步已经使得研究单个量子小系统的热力学成为可能。不同于宏观情况，涨落，包括量子和热涨落，是量子小系统和外界进行能量交换的重要特征。在此背景下，《量子轨迹随机热力学：涨落的功、热及其应用》致力于探索量子小系统随机的功、热、熵产生等的物理和数学规律。本项目以量子物理为基础，随机数学为手段，重点研究封闭系统量子功的性质以及开放系统量子跳跃轨迹的随机热力学理论，得到两个方面的重要成果。在封闭量子体系中，确立量子功满足量子-经典对应原理；提出相空间中力迫量子谐振子功特征函数计算的解析理论；得到量子功特征函数近似到普朗克常数二阶的一般公式及物理解释，并发展出有效的数值计算方法。在开放量子体系，运用量子跳跃轨迹概念澄清开系统量子Feynman-Kac公式的概率起源；建立了自洽的基于量子跳跃轨迹的量子随机热力学理论并应用于量子随机热机的效率研究；证明该理论和基于系统-环境封闭系统两次测量构建的随机热力学在数学上等价；在量子主方程系统中发现一个新的涨落定理。本项目的开展不仅极大深化了对量子随机热力学基本概念、物理性质、数学结构的认识，也为正在进行中的量子机器实验研究提供了坚实的理论基础。