  We study a process of anomalous diffusion, based on intermittent velocity
fluctuations, and we show that its scaling depends on whether we observe the
motion of many independent trajectories or that of a Liouville-like equation
driven density. The reason for this discrepancy seems to be that the
Liouville-like equation is unable to reproduce the multi-scaling properties
emerging from trajectory dynamics. We argue that this conflict between density
and trajectory might help us to define the uncertain border between dynamics
and thermodynamics, and that between quantum and classical physics as well.
