The statistical physics of Cities

TL;DR

This paper explores how statistical physics provides a framework for understanding and modeling key phenomena in urban systems, aiding policy development for sustainable city growth.

Contribution

It introduces a physics-inspired approach to analyze urban population distribution, segregation, polycentricity, mobility, and scaling laws in cities.

Findings

Urban population distributions follow specific statistical patterns.

Segregation phenomena can be modeled using spin-like models.

Scaling laws describe socio-economic and infrastructural growth in cities.

Abstract

Challenges due to the rapid urbanization of the world -- especially in emerging countries -- range from an increasing dependence on energy, to air pollution, socio-spatial inequalities, environmental and sustainability issues. Modelling the structure and evolution of cities is therefore critical because policy makers need robust theories and new paradigms for mitigating these problems. Fortunately, the increased data available about urban systems opens the possibility of constructing a quantitative 'science of cities', with the aim of identifying and modelling essential phenomena. Statistical physics plays a major role in this effort by bringing tools and concepts able to bridge theory and empirical results. This article illustrates this point by focusing on fundamental objects in cities: the distribution of the urban population; segregation phenomena and spin-like models; the polycentric transition of the activity organization; energy considerations about mobility and models inspired by gravity and radiation concepts; CO2 emitted by transport; and finally, scaling that describes how various socio-economical and infrastructures evolve when cities grow.