Expansion, Thermalization and Entropy Production in High-Energy Nuclear Collisions

Abstract

The thermalization process is studied in an expanding parton gas using the Boltzmann equation with two types of collision terms. In the relaxation time approximation we determine the criteria under which a time-dependent relaxation time leads to thermalization of the partons. We calculate the entropy production due to collisions for the general time-dependent relaxation time. In a perturbative QCD approach on the other hand, we can estimate the parton collision time and its dependence on expansion time. The effective `out of equilibrium' collision time differs from the standard transport relaxation time, $τ_{\rm tr}\simeq(α_s^2\ln(1/α_s)T)^{-1}$, by a weak time dependence. It is in both cases Debye screening and Landau damping that regulate the singular forward scattering processes. We find that the parton gas does thermalize eventually but only after having undergone a phase of free streaming and gradual equilibration where considerable entropy is produced (``after-burning"). The final entropy and thus particle density depends on the collision time as well as the initial conditions (a ``memory effect"). Results for entropy production are presented based upon various model estimates of early parton production.