  We present a theory for the description of energy relaxation in a
nonequilibrium condensate of bosonic particles. The approach is based on
coupling to a thermal bath of other particles (e.g., phonons in a crystal, or
noncondensed atoms in a cold atom system), which are treated with a Monte Carlo
type approach. Together with a full account of particle-particle interactions,
dynamic driving, and particle loss, this offers a complete description of
recent experiments in which Bose-Einstein condensates are seen to relax their
energy as they propagate in real space and time. As an example, we apply the
theory to the solid-state system of microcavity exciton polaritons, in which
nonequilibrium effects are particularly prominent.
