The rank-size scaling law and entropy-maximizing principle

doi:10.1016/j.physa.2011.07.010

CORC > 北京大学 > 地球与空间科学学院

	The rank-size scaling law and entropy-maximizing principle
	Chen, Yanguang
刊名	physica a statistical mechanics and its applications
	2012
关键词	Urban system Rank-size rule Zipf&apos Fractals Fractal dimension Scaling range Hierarchy Entropy-maximizing method SELF-ORGANIZED CRITICALITY URBAN-GROWTH PATTERNS ZIPFS LAW CITIES HIERARCHIES MODELS RULE DERIVATIONS POPULATION s law
DOI	10.1016/j.physa.2011.07.010
英文摘要	The rank-size regularity known as Zipf's law is one of the scaling laws and is frequently observed in the natural living world and social institutions. Many scientists have tried to derive the rank-size scaling relation through entropy-maximizing methods, but they have not been entirely successful. By introducing a pivotal constraint condition. I present here a set of new derivations based on the self-similar hierarchy of cities. First. I derive a pair of exponent laws by postulating local entropy maximizing. From the two exponential laws follows a general hierarchical scaling law, which implies the general form of Zipf's law. Second. I derive a special hierarchical scaling law with the exponent equal to 1 by postulating global entropy maximizing, and this implies the pure form of Zipf's law. The rank-size scaling law has proven to be one of the special cases of the hierarchical scaling law, and the derivation suggests a certain scaling range with the first or the last data point as an outlier. The entropy maximization of social systems differs from the notion of entropy increase in thermodynamics. For urban systems, entropy maximizing suggests the greatest equilibrium between equity for parts/individuals and efficiency of the whole. (C) 2011 Elsevier B.V. All rights reserved.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000297779500036&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Physics, Multidisciplinary; SCI(E); EI; SSCI; 15; ARTICLE; 3; 767-778; 391
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/161051]
专题	地球与空间科学学院
推荐引用方式 GB/T 7714	Chen, Yanguang. The rank-size scaling law and entropy-maximizing principle[J]. physica a statistical mechanics and its applications,2012.
APA	Chen, Yanguang.(2012).The rank-size scaling law and entropy-maximizing principle.physica a statistical mechanics and its applications.
MLA	Chen, Yanguang."The rank-size scaling law and entropy-maximizing principle".physica a statistical mechanics and its applications (2012).