  We study the abundance of a particle species in a thermalized plasma by
introducing a quantum kinetic description based on the non-equilibrium
effective action. A stochastic interpretation of quantum kinetics in terms of a
Langevin equation emerges naturally. We consider a particle species that is
stable in the vacuum and interacts with \emph{heavier} particles that
constitute a thermal bath in equilibrium and define of a fully renormalized
single particle distribution function. The distribution function thermalizes on
a time scale determined by the \emph{quasiparticle} relaxation rate. The
equilibrium distribution function depends on the full spectral density and
features off-shell contributions to the particle abundance. A model of a
bosonic field $\Phi$ in interaction with two \emph{heavier} bosonic fields is
studied. We find substantial departures from the Bose-Einstein result both in
the high temperature and the low temperature but high momentum region. In the
latter the abundance is exponentially suppressed but larger than the
Bose-Einstein result. We obtain the Boltzmann equation in renormalized
perturbation theory and highlight the origin of the differences. We argue that
the corrections to the abundance of cold dark matter candidates are
observationally negligible and that recombination erases any possible spectral
distortions of the CMB. However we expect that the enhancement at high
temperature may be important for baryogenesis.
