Urbanization, Energy Consumption and Entropy of Metropolises
Syed Amaar Ahmad
Senior Member, IEEE
syed.a.ahmad@ieee.org
Abstract
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 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 power-demand 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.
Keywords: complex systems; Pareto-optimality; topological invariance; multi-scalar information; cellular automata; Dyson civilization
Cite this publication as:
S. A. Ahmad, “Urbanization, Energy Consumption and Entropy of Metropolises,”
Complex Systems, 28(3), 2019 pp. 287–312.
https://doi.org/10.25088/ComplexSystems.28.3.287
