Statistical laws in urban mobility from microscopic GPS data in the area of Florence

The application of Statistical Physics to social systems is mainly related to the search for macroscopic laws that can be derived from experimental data averaged in time or space, assuming the system in a steady state. One of the major goals would be to find a connection between the statistical laws and the microscopic properties: for example, to understand the nature of the microscopic interactions or to point out the existence of interaction networks. Probability theory suggests the existence of a few classes of stationary distributions in the thermodynamics limit, so that the question is if a statistical physics approach could be able to enroll the complex nature of the social systems. We have analyzed a large GPS database for single-vehicle mobility in the Florence urban area, obtaining statistical laws for path lengths, for activity downtimes and for activity degrees. We show also that simple generic assumptions on the microscopic behavior could explain the existence of stationary macroscopic laws, with a universal function describing the distribution. Our conclusion is that understanding the system complexity requires a dynamical database for the microscopic evolution, which allows us to solve both small space and time scales in order to study the transients.