  We propose a phenomenological non-equilibrium framework for modelling the
evolution of cities which describes the intra-urban resettlement as an
irreversible diffusive process. We validate this framework using the actual
migration data for the Australian capital cities. With respect to the
residential relocation, the population is shown to be composed of two distinct
groups, exhibiting different relocation frequencies. In the context of the
developed framework, these groups can be interpreted as two components of a
binary mixture, each with its own diffusive relaxation time. Using this
approach, we obtain long-term predictions of the cities' spatial structure,
which defines their equilibrium population distribution.
