Potential field theory for spatial dynamics: a continuous framework for modelling socioeconomic processes

This paper develops a continuous potential field framework for analysing the direction, intensity and topology of socio-economic flows, whether driven by migration, capital, labour or innovation. Rather than relying on bilateral exchanges or correlations across spatial units, it reconstructs a differentiable attractiveness surface from movements and interprets redistribution as motion along its gradient. Applied to central Italy’s gridded demographic data, the framework reveals a polarised geography of repulsive inner areas and metropolitan attraction basins. A comparison with a separately derived income field shows that economic incentives explain only part of observed movements, pointing to a role for non-monetary frictions.