  The thermalization of the particles produced in collisions of small size
objects can be achieved by quantum entanglement of the partons of the initial
state as it was analyzed recently in proton-proton collisions. We extend such
study to Pb-Pb collisions and to different multiplicities of proton-proton
collisions. We observe that, in all cases, the effective temperature is
approximately proportional to the hard scale of the collision. We show that
such relation between the thermalization temperature and the hard scale can be
explained as a consequence of the clustering of the color sources. The
fluctuations on the number of parton states decreases with multiplicity in
Pb-Pb collisions as far as the width of the transverse momentum distributions
decreases, contrary to the p-p case. We relate these fluctuations to the
temperature time fluctuations by means of a Langevin equation for the white
noise due to the quench of a hard parton collision.
