  We investigate the conditions under which particle multiplicities in high
energy collisions are Boltzmann distributed, as is the case for hadron
production in e^+e^-, pp, p-pbar and heavy ion collisions. We show that the
apparent temperature governing this distribution does not necessarily imply
equilibrium (thermal or chemical) in the usual sense, as we explain. We discuss
an explicit example using tree level amplitudes for N photon production in
which a Boltzmann-like distribution is obtained without any equilibration. We
argue that the failure of statistical techniques based on free particle
ensembles may provide a signal for collective phenomena (such as large shifts
in masses and widths of resonances) related to the QCD phase transition.
