论流域系统稳定性的判别指标——超熵

Superentropy-a Criterion for Determining Stability of Drainage System

在“侵蚀流域系统的信息熵”一文中,我们在伊凡诺夫曲线的基础上,将信息熵由侵蚀流域引入了一般流域;而后,在“再论流域系统信息熵”一文中,证明了斯特拉勒曲线在流域系统内外营力作用大致相等时处于瞬时平衡的形态特征,从而将线性平衡态熵引入了流域系统研究。但就一般情况而言,流域系统是远离平衡态的耗散结构,这要求进一步研究流域系统的非线性、非平衡态熵。为了解决这一问题,我们引入了超熵概念。在探讨实际问题时,我们往往会遇到各种复杂的体系,对此,可将它们归并为包含一个子系统的体系和包含多个子系统的体系两种情形,并导出了适合于单子系统体系的超熵表达式: (?)_xP=[-βα~3(α~2-1)]\[α(-β-1)-3]和对多于系统体系适用的超熵表达式: (?)_xP=kP-∑|Pi-P|将它们分别应用于滑坡,泥石流和地震的研究,得出了非常满意的结果。

The authers developed comentropy from an erosional drainage into a general one in'Comentropy in Erosional Drainage-System'(Ai, 1987), discussed in'Further Study on Comentropy in Drainage-System', the characteristics of Straler's hypsometric curve when the endogenic and exogenic forces are almost the same and the system is in an instantneous equilibrium state,and introduced linear equilibrium entropy into drainage system study.However, a drainage-system is generally a dissipation structure, being far from equilibrium state.Thus,the entropy should be studied when the system is in a nonlinear and non-equilibrium state.To solve this problem, we import super-entropy. We often encounter various systems in actual studies, but we can divide these systems into two kinds: a system containing one subsystem and a system containing more than one subsystem.The authors deduce the super-entropy expression of the system containing only one subsystem as (?)_xP=(-βα~3(α-1)(α+1))/α(-β-1)^(-3) and the superentropy expression of the system containing more than one subsystem as: We use the two expressions in studies such as landslides,debris-flows and earthquakes, the results in this paper are very satisfying.