We describe the transition of N weakly interacting atoms into a
Bose-Einstein condensate within a number-conserving quantum master equation
theory. Based on the separation of time scales for condensate formation and
non-condensate thermalization, we derive a master equation for the condensate
subsystem in the presence of the non-condensate environment under the inclusion
of all two body interaction processes. We numerically monitor the condensate
particle number distribution during condensate formation, and derive a
condition under which the unique equilibrium steady state of a dilute, weakly
interacting Bose-Einstein condensate is given by a Gibbs-Boltzmann thermal
state of N non-interacting atoms
