摘要翻译：
我们考虑了大都市城市是一个由社会网络、工程系统、农业产出、经济活动和能源组成的混合复杂系统，其能耗的标度律、二阶统计量和熵。我们用两个基本变量来抽象一个城市；表示耗能地理或空间区域（例如土地、住房或基础设施等）的$S$资源单元（单位面积）和由可在这些单元之间迁移的$N$移动单元组成的人口。研究表明，当大都市面积不变($S$)时，耗能的方差和熵随着$N$的增加而增加，达到最大值，然后随着饱和度的增加而减小到零。这些指标是人口空间流动性的指标。在一定情况下，方差有界为大都市平均耗能的二次函数。但是，当人口和大都市区是内生的时，当人口密度降低时，大都市区的增长受到抑制。相反，当$n\geq{s}\log{n}$或当人口过多和人口不足地区的总和都很大时，人口增长达到平衡。此外，当一个大都市的子区域之间的经济依赖是基于能源消耗熵时，我们还得出了我们的方法与多标量信息之间的关系。最后，如果城市的经济规模（国内产品等）与消耗的能源成正比，那么在人口密度不变的情况下，我们证明了经济规模与表面积（或$S$)成线性关系。
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英文标题：
《On Metropolis Growth》
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作者：
Syed Amaar Ahmad
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最新提交年份：
2017
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分类信息：

一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
  We consider the scaling laws, second-order statistics and entropy of the consumed energy of metropolis cities which are hybrid complex systems comprising social networks, engineering systems, agricultural output, economic activity and energy components. We abstract a city in terms of two fundamental variables; $s$ resource cells (of unit area) that represent energy-consuming geographic or spatial zones (e.g. land, housing or infrastructure etc.) and a population comprising $n$ mobile units that can migrate between these cells. We show that with a constant metropolis area (fixed $s$), the variance and entropy of consumed energy initially increase with $n$, reach a maximum and then eventually diminish to zero as saturation is reached. These metrics are indicators of the spatial mobility of the population. Under certain situations, the variance is bounded as a quadratic function of the mean consumed energy of the metropolis. However, when population and metropolis area are endogenous, growth in the latter is arrested when $n\leq\frac{s}{2}\log(s)$ due to diminished population density. Conversely, the population growth reaches equilibrium when $n\geq {s}\log{n}$ or equivalently when the aggregate of both over-populated and under-populated areas is large. Moreover, we also draw the relationship between our approach and multi-scalar information, when economic dependency between a metropolis's sub-regions is based on the entropy of consumed energy. Finally, if the city's economic size (domestic product etc.) is proportional to the consumed energy, then for a constant population density, we show that the economy scales linearly with the surface area (or $s$).
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PDF链接：
https://arxiv.org/pdf/1712.02937