On critical dynamics and thermodynamic efficiency of urban transformations

TL;DR

This paper models urban transformations using a statistical-mechanical approach, identifying critical regimes and phase transitions, and introduces a thermodynamic efficiency measure maximized at critical points.

Contribution

It develops a novel thermodynamic framework for urban dynamics, linking phase transitions with the efficiency of urban transformations.

Findings

Identifies phase transitions between dispersed and polycentric urban phases.

Quantifies the thermodynamic cost of urban change using Fisher information.

Shows thermodynamic efficiency peaks at critical regimes.

Abstract

Urban transformations within large and growing metropolitan areas often generate critical dynamics affecting social interactions, transport connectivity and income flow distribution. We develop a statistical-mechanical model of urban transformations, exemplified for Greater Sydney, and derive a thermodynamic description highlighting critical regimes. We consider urban dynamics at two time scales: fast dynamics for the distribution of population and income, modelled via the maximum entropy principle, and slower dynamics evolving the urban structure under spatially distributed competition. We identify phase transitions between dispersed and polycentric phases, induced by varying the social disposition---a factor balancing the suburbs' attractiveness---in contrast with the travel impedance. Using the Fisher information we identify critical thresholds and quantify the thermodynamic cost of urban transformation, as the minimal work required to vary the underlying parameter. Finally, we introduce the notion of thermodynamic efficiency of urban transformation, as the ratio of the order gained during a change to the amount of required work, showing that this measure is maximised at criticality.