小系统中的反常扩散和Kramers逃逸问题研究

项目名称： 小系统中的反常扩散和Kramers逃逸问题研究

项目编号： No.11505103

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 王春阳

作者单位： 鲁东大学

项目金额： 20万元

中文摘要： 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。

中文关键词： 反常扩散；Kramers；逃逸；小系统；朗之万方程

英文摘要： 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.

英文关键词： anomalous diffusion;Kramers escaping;small system;Langevin equation