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Urban transformations within large and growing metropolitan areas oftengenerate critical dynamics affecting social interactions, transportconnectivity and income flow distribution. We develop a statistical-mechanicalmodel of urban transformations, exemplified for Greater Sydney, and derive athermodynamic description highlighting critical regimes. We consider urbandynamics at two time scales: fast dynamics for the distribution of populationand income, modelled via the maximum entropy principle, and slower dynamicsevolving the urban structure under spatially distributed competition. Weidentify phase transitions between dispersed and polycentric phases, induced byvarying the social disposition---a factor balancing the suburbs'attractiveness---in contrast with the travel impedance. Using the Fisherinformation we identify critical thresholds and quantify the thermodynamic costof urban transformation, as the minimal work required to vary the underlyingparameter. Finally, we introduce the notion of thermodynamic efficiency ofurban transformation, as the ratio of the order gained during a change to theamount of required work, showing that this measure is maximised at criticality.

On critical dynamics and thermodynamic efficiency of urban transformations