Traffic and Crowd Dynamics: The Physics of the City

In this contribution we describe the crowd and tra±c dynamics, modeling complex urban mobility. The pioneer investigations of I. Prigogine with a thermodynamical point of view (1960), and M. Batty with a dynamical approach (1971), are, in our opinion, the progenitors for a new theoretical look to the urban phenomena in a complex conceptual framework. Some features characterizing complexity are the non-linearity of the involved phenomena, a far from equilibrium statistical evolution, the network structure, the role of information, the emergence properties and the self-organization. When we study the urban mobility all these properties appear. Moreover also the elementary components of the urban systems, i.e. the citizens, are complex since they possess both a cognitive behavior and a physical dynamics. So the crowding and tra±c phenomena are an excellent laboratory in order to understand, describe and model complexity. Finally studying crowding and tra±c, there needs a new knowledge power in simulation to perform virtual experiments able to predict criticalities, like transitions from order to chaos, and to detect control parameters for the system governance. 3