Towards a Statistical Mechanics of Cities

Abstract

Cities are some of the most complex dynamical systems in human societies and in nature. There is growing interest in producing more comprehensive quantitative theory, capable of describing many of the features now observable in urban environments, especially those that show empirical regularities across cities of different sizes, geographies, and levels of development. The principal challenge of achieving such a goal is our ability to build frameworks that include realistic but simple accounts of agents’ choices and strategic behavior, beyond current approaches in statistical physics or economics. Here, I propose a general framework that integrates agents’ behavior with their resource and information management towards seizing opportunities in their environment. I show how this approach integrates urban scaling theory with a statistical mechanics of open-ended (economic) growth. The framework is general and, with appropriate modifications and elaborations, can account for the statistical dynamics of other complex systems.