Thermodynamics of urban growth revealed by city scaling

Abstract

Cities are complex systems, where micro-scale phenomena lead to emergent, macro-scale patterns. Scaling in cities – the study of how characteristics of cities change with urban population – has been explained based on social interactions and networks, but cities are also governed by the laws of physics, such as thermodynamics and conservation of mass. Here we explore scaling laws in the context of the city as a far-from-equilibrium thermodynamic system, showing how scaling phenomena are consistent with ideas of cities as dissipative systems, the emergence of higher-order structures, and the Maximum Power Principle. We theorize that as cities grow, they use an increasing amount of energy and resources to produce an incremental change in useful work done. Furthermore, they require additional energy and materials to build higher-order structures, such as transportation systems, to overcome increasing density and congestion. We support our theoretical approach with new empirically observed scaling relationships.