  We demonstrate that a new type of analysis in heavy-ion collisions, based on
an event-by-event analysis of the transverse momentum distribution, allows us
to obtain information on secondary interactions and collective behaviour that
is not available from the inclusive spectra. Using a random walk model as a
simple phenomenological description of initial state scattering in collisions
with heavy nuclei, we show that the event-by-event measurement allows a
quantitative determination of this effect, well within the resolution
achievable with the new generation of large acceptance hadron spectrometers.
The preliminary data of the NA49 collaboration on transverse momentum
fluctuations indicate qualitatively different behaviour than that obtained
within the random walk model. The results are discussed in relation to the
thermodynamic and hydrodynamic description of nuclear collisions.
