A Prehistorical Approach to Optimal Fluctuations for General Langevin Dynamics with Weak Gaussian White Noises

Author:

Zhao FengORCID,Li YangORCID,Liu Xianbin

Abstract

The dynamics of a stochastic system that exhibits large fluctuations to a given state are almost deterministic due to weak random perturbations. Such large fluctuations occur with overwhelming probability in the vicinity of the so-called optimal path, which is a vital concept in physics, chemistry, and biology, as it uncovers the way in which a physical process escapes from the attractive domain of a metastable state and transitions between different metastable states. In this paper, we examine the prehistorical description of the optimal fluctuation with the unifying framework of Langevin dynamics by means of a quantity called prehistory probability density. We show that the optimal fluctuation has a strong connection with the time reversal of the associated diffusion process. Specifically, in the stationary or quasi-stationary cases, it is found that the prehistory probability density actually acts as the transition probability density of the reversed process. As noise intensity approaches zero, it focuses on the average dynamics of the reversed process due to the law of large numbers, which is then shown to coincide with the time reversal of the optimal path. The local dispersion of the prehistory probability density can thus be reformulated as a Gaussian distribution corresponding to the linearized part of the reversed process. In addition, as an analogue of the original definition in the stationary states, it is proven that the concept of prehistory probability density can also be extended to nonstationary cases where similar properties are still valid. Based on these theoretical results, an algorithm is designed and then successfully applied to a one-dimensional example at the end, showing its accuracy for pinpointing the location of the optimal path and its efficacy in cases where multiple optimal paths coexist.

Funder

National Natural Science Foundation of China

Publisher

MDPI AG

Subject

Fluid Flow and Transfer Processes,Computer Science Applications,Process Chemistry and Technology,General Engineering,Instrumentation,General Materials Science

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3