小系统中的反常扩散和Kramers逃逸问题研究

The non-equilibrium and stochastic thermodynamics of small systems is a front hot issue in recent years. Although Evans-Searles fluctuation theorem and Jarzynski formula are expressed in very beautiful forms, but they are not kinetic equations. In application, it is difficult to use them as a starting point to deal adequately with physical realities. For a better revealing on the non-equilibrium and stochastic thermodynamic properties of small systems. The project plan to make a in-depth study on the anomalous diffusion, Kramers escaping and related stochastic thermodynamic problems of small systems in the context of fractional Brown motions. The method we are using is based on the Langevin statistical dynamics. With the execution of this project, we hope to be able to clearly reveal the anomalous transport mechanism and stochastic thermodynamic laws of small systems, extend theoretically the classical thermodynamic knowledges about Brownian motion of classical thermodynamics to small systems, provide useful information as more as possible for the scientific researching works in the field of nano-science, chemical reaction and biophysics.

小系统的非平衡和随机热力学是近年来的一个前沿热点问题。Evans-Searles涨落定理和Jarzynski等式形式上虽然漂亮，但由于它们不是动力学方程，理论上很难以它们作为出发点来处理实际问题。为更好地研究小系统的随机热力学性质，本项目拟在分数布朗运动的背景下，使用朗之万统计动力学方法，深入地研究一维和二维小系统中的反常扩散、Kramers逃逸和有关的随机热力学问题。通过本项目的开展，揭示小系统中的反常输运机制和随机热力学规律，将布朗运动有关的古典热力学知识推广至小系统，以所得结果为纳米科学、化学反应物理学和生物物理等领域有关问题的研究提供尽可能多的有用信息。

本项目按计划对小系统中的反常扩散和Kramers逃逸等有关的随机热力学问题进行了较为深入的研究。通过引入分数阶阻尼来表达小系统的奇异特性，发现了粒子在扩散过程中会出现较为明显的逆向运动以及粒子在鞍点附近区域的迂回现象明显地减弱等反常统计现象，并对使用朗之万动力学方法对造成这些结果的原因进行了分析与探讨，获得了一些比较重要的发现和研究结论，在一定程度上揭示出了小系统中的反常输运机制和随机热力学规律。为将布朗运动有关的古典热力学知识推广至小系统并进行相关拓展提供了一些有用信息，基本实现了预期的研究目标。