Kangning Huang & Mingzhen Lu 
Nature Cities (2026)

A long-standing puzzle in urban science is whether there is an intrinsic match between human populations and the mass of their built environments. Existing models assume proportionality: each additional resident demands the same amount of building material. Our analysis of more than 3,000 cities worldwide challenges this linear assumption. Built mass grows more slowly than population (that is, sublinear scaling), across cities (β = 0.90) and across neighborhoods within a city (δ = 0.75). This means that larger cities and denser neighborhoods achieve economies of scale with less per capita built mass. Our theoretical framework further shows that the across-city scaling pattern emerges from the uneven within-city distribution of people. These findings caution against well-meaning interventions, such as height and building-size limits, that artificially flatten cities’ natural density gradients. Effective urban policy should instead move beyond per capita linear thinking, adopting scale-adjusted metrics and managing cities as nested complex systems.A long-standing puzzle in urban science is whether there is an intrinsic match between human populations and the mass of their built environments. Existing models assume proportionality: each additional resident demands the same amount of building material. Our analysis of more than 3,000 cities worldwide challenges this linear assumption. Built mass grows more slowly than population (that is, sublinear scaling), across cities (β = 0.90) and across neighborhoods within a city (δ = 0.75). This means that larger cities and denser neighborhoods achieve economies of scale with less per capita built mass. Our theoretical framework further shows that the across-city scaling pattern emerges from the uneven within-city distribution of people. These findings caution against well-meaning interventions, such as height and building-size limits, that artificially flatten cities’ natural density gradients. Effective urban policy should instead move beyond per capita linear thinking, adopting scale-adjusted metrics and managing cities as nested complex systems.

Read the full article at: www.nature.com

Andrea Filippo Beretta, Manlio De Domenico

Understanding how complex networks respond to perturbations is key to uncovering their functional organization. We show that, for a maximum-entropy perturbation prior, standard diffusion cannot increase response entropy, a measure of the diversity of the system’s response. To overcome this limitation, we develop a density-matrix-based information thermodynamics of perturbation responses along arbitrary dynamical trajectories. We show that this framework is grounded in an information-theoretic principle of least dissipation and introduces a generalized free energy that quantifies deviations from an instantaneous diffusive reference. We then illustrate the formalism using nonlinear complex networks, revealing regimes of enhanced response diversity that cannot be captured by standard diffusive descriptions.

Read the full article at: arxiv.org