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We propose a phenomenological non-equilibrium framework for modelling theevolution of cities which describes the intra-urban resettlement as anirreversible diffusive process. We validate this framework using the actualmigration data for the Australian capital cities. With respect to theresidential relocation, the population is shown to be composed of two distinctgroups, exhibiting different relocation frequencies. In the context of thedeveloped framework, these groups can be interpreted as two components of abinary mixture, each with its own diffusive relaxation time. Using thisapproach, we obtain long-term predictions of the cities' spatial structure,which defines their equilibrium population distribution.

Diffusive resettlement: irreversible urban transitions in closed systems