随机热机热力学及性能研究

Non-equilibrium thermodynamics and statistical behavior of small systems have attracted much attention in recent years. In this project we intend to perform the research in the following issues: (1) Given a stochastic system, we will derive thesystem-dependent analytical expressions of the entropy, heat and work, and obtain the expression for entropy production rate during the corresponding process, finding the expressions of the performance parameters for the heat engine. (2) We will study the efficiency at maximum power (compared with CA efficiency) and the power corresponding to the maximum efficiency, with special emphasis on the possibility that the Carnot efficiency might be achieved with finite power. (3) With the framework of the stochastic thermodynamics and irreversible thermodynamics, we will study the thermodynamics of a stochastic heat engine in the nonlinear response regime. (4) Based on models of heat engines near critical point or under information feedback, we will investigate its possibly novel performance characteristics, revealing the physical nature of the universality of the second law of thermodynamics. As a natural extension, we will turn to the analysis of the performance characteristics of the refrigerators. In one word, in this project we will focus on the study of the performance and thermodynamics of various stochastic heat engines, which will help us to reveal the novel thermodynamics and statistical behavior due to fluctuations and quantum effects of small systems.

随机小系统的非平衡热力学和统计行为，近年来已引起人们的极大关注。本项目拟进行如下研究：（1）给定随机系统，给出系统的熵、热量、功的含时解析式，得到非平衡热力学过程中熵产率的表示，从而得到热机性能参数；（2）研究随机热机的最大功率下的效率（和CA效率比对分析）的普适性和最大效率下的功率，重点分析效率达到卡诺效率但输出功率不为零的可能性； （3）结合随机热力学和不可逆热力学理论方法，分析非线性响应区域下的随机热机的热力学性质；（4）研究临界热机和信息反馈下的随机热机的新奇性能，并以此模型探究热力学第二定律的普适性问题。进一步地，拓展到（低温）制冷机模型，分析制冷机的性能特征。总之，本项目将集中研究随机的热力学及性能，并解释小系统涨落和量子效应等导致的新奇热力学和统计行为。

不同于宏观开放系统热和功——两表征能量交换的物理量均为确定的，微观开放系统热和功均随机量。因此，以微/介观系统为工作物质的热机的输出效率和功率也是随机物理量，两者的涨落不可忽略。基于随机热力学理论框架，项目主要进行了如下三方面的研究：（1）构建微纳尺度热机模型，研究有限（小）开放系统为工质的热机(工作于线性和非线性响应区域）有限功率下的性能特征，分析效率、功率以及涨落之间的约束关系，揭示热机的刻画热机稳定性的微观物理机制,讨论了最大输出功率下效率的普适性。（2）分析上述热机时，探讨系统本身反直觉行为（Mpemba效应）或者热源的量子尺度（具有量子压缩）等对热机的随机热力学及性能特征的影响，阐述此类热机新奇性能特征和新奇热力学性质。（3）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，分析能量量子化对量子力学机的效率和功率的影响。研究表明，能量量子化可以提高量子力学机的性能。本项目的研究结果阐明了微纳尺度热机的一些随机热力学性质和新奇性能特征。