Urbanization, Energy Consumption and Entropy of Metropolises
Metropolises are complex systems comprising social networks, engineering systems, agricultural output, economic activity and energy components. Urbanization stems from both increasing human population levels and expansion in a city's surface area. In this paper, we develop a model of how the population and area of a city affect its energy consumption patterns. We also show that with urbanization of smaller cities, there is a corresponding increase in the entropy (or variance) of the energy
... of the energy consumption, whereas, for larger cities, the entropy actually diminishes. This result interestingly implies that as metropolises scale, we may have a way to determine the point of a city's stagnation or decline. In the empirical analysis, we use powerdemand data from the island state of Singapore between 2004 and 2019 to illustrate that with population growth, there is a tipping point for variance (or equivalently entropy) in the power demand. Moreover, we also provide a theoretical framework on how population growth and area growth cycles are mutually dependent and expand on how much information can be extracted about the entire city from a subregion. Finally, we show that if the city's economic size (domestic product etc.) is proportional to the consumed energy, then for a constant population density, the economy scales linearly with the area. Our effort in developing a metropolis growth model is motivated by the need to understand how human behavior and organization at scale affect sustainability and economic growth.