On the existence of potential landscape in the evolution of complex systems
On the existence of potential landscape in the evolution of complex systems
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DOI：
10.1002/cplx.20171
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发表时间：
2007-03-01
期刊：
影响因子：
2.3
通讯作者：
Qian, Hong
中科院分区：
文献类型：
--
作者：
Ao, Ping;Kwon, Chulan;Qian, Hong
最近发展起来的对随机过程的处理导致了复杂系统动态演化的潜在图景的构建。由于一般环境中势函数的存在在文献中经常受到质疑，这里我们研究几个相关的理论问题，这些问题是构造的核心。我们表明，通过变换，这种新的处理方法与辛结构密切相关，辛结构在理论物理的许多分支中都是中心。利用这一观点，我们证明了变换下的一个不变量。在一维情形下，我们进一步明确地证明了新的处理方法与Ito和Stratonovich以及其他人的处理方法之间的对比。我们的结果有力地表明，统计物理学的方法在研究随机、复杂系统中是有用的。(C)2007年威利期刊公司。
A recently developed treatment of stochastic processes leads to the construction of a potential landscape for the dynamical evolution of complex systems. Since the existence of a potential function in generic settings has been frequently questioned in literature, here we study several related theoretical issues that lie at core of the construction. We show that the novel treatment, via a transformation, is closely related to the symplectic structure that is central in many branches of theoretical physics. Using this insight, we demonstrate an invariant under the transformation. We further explicitly demonstrate, in one-dimensional case, the contradistinction among the new treatment to those of Ito and Stratonovich, as well as others. Our results strongly suggest that the method from statistical physics can be useful in studying stochastic, complex systems in general. (c) 2007 Wiley Periodicals, Inc.