以有限系统为工质的量子热力学循环性能的理论研究

Quantum effects and thermal fluctuations as well as dissipation are of significance in finite (small) quantum systems, which have attached much attention in recent years. Based on our previous work within the related topic, in this project we intend to study the performance in finite time of quantum heat engines or refrigerators which use finite (small) system as the working substance. Within the framework of both finite-time thermodynamics and irreversible thermodynamics, we will perform our research in the following issues: (1) We will derive for any given thermodynamic process the generally analytical expressions of the entropy production, and obtain the universal expression for entropy production rate during an “adiabatic” process with non-adiabatic dissipation. We then study the performance of quantum heat engines with internal non-adiabatic dissipations. (2)Considering the effects induced by interactions [e.g.,quantum coherence (de-coherence) and entanglement], we will investigate the performance of quantum heat engines based on (open) finite systems and disclose the possible universal feature of efficiency at maximum power. (3) Extending from heat engines to refrigerators, we will analyze the performance characteristics by optimizing the cooling rate and coefficient of performance. When the temperature is low, we will propose to reveal the physical nature of the third law of thermodynamics, and discuss the effects induced by phase transition on the performance characteristics of quantum refrigerators. In one word, in this project we will study the performance in finite time of various quantum thermodynamic cycles that work with finite (small) systems, which will help us to reveal the novel quantum effects as well as thermodynamic behaviors of finite quantum systems, and also understand the relationship between the finite-time thermodynamics and irreversible thermodynamics.

量子效应、热涨落和耗散在有限（小）系统中具有重要意义，近来已引起人们的极大关注。 作为我们目前研究工作的自然延伸， 本项目将继续研究以有限系统为工质的量子热机或制冷机的性能特征。结合有限时间热力学和不可逆热力学理论，我们将进行如下三方面的研究：（1）给出有限量子系统熵的含时一般解析式，得到到非绝热耗散存在的“绝热”过程熵产率的普适表示,分析具有非绝热耗散的热机性能；（2） 考虑有限量子系统存在相互作用（如量子相干、量子纠缠和退相干等）时，研究有限（小）开放系统为工质的量子热机的性能特征，并揭示最大输出功率下效率的普适性；（3）将热机拓展到（低温）制冷机模型， 优化制冷机的制冷率和制冷系数等性能参数以分析其性能特征。总之，我们将研究以有限系统为工质的量子热力学循环的性能特征，解释有限量子系统的新奇量子效应和热力学行为，并揭示有限时间热力学和不可逆热力学理论之间的联系。

有限尺寸效应、量子效应、涨落以及耗散等在有限（小）系统中具有重要意义。本项目我们研究以有限系统为工质的量子热机或制冷机的性能特征。结合有限时间热力学和不可逆热力学理论，我们将进行如下两方面的研究：（1）以囚禁单粒子为工作物质，不引入温度概念，构建量子力学机模型，通过分析效率和功率来研究该量子力学机的性能特征。研究表明，此类量子力学机的最大输出功率下效率的解析表示具有一定的普适性。（2）基于有限时间热力学和不可逆热力学理论框架，研究有限（小）开放系统为工质的量子热机和制冷机(工作于线性和非线性响应区域）有限功率下的性能特征，重点分析最大输出功率下效率的普适性。本项目的研究结果揭示了有限尺寸、量子本质和量子相变等对量子热机（制冷机）的性能特征的影响。所得结果有助于理解有限量子系统的新奇热力学和统计行为，并揭示了有限时间热力学和不可逆热力学理论之间的联系。