  We study the thermalization of a scalar field $\Phi$ coupled to two other
scalar fields $\chi_{1,2}$ that constitute a bath in thermal equilibrium. For a
range of masses the $\Phi$ propagator features threshold and infrared
divergences, a vanishing residue at the (quasi) particle pole and vanishing
\emph{on-shell} decay rates thereby preventing the equilibration of $\Phi$ with
the bath via on-shell processes. Inspired by the theory of quantum open systems
we obtain a quantum master equation for the reduced density matrix of $\Phi$
that includes the time dependence of bath correlations, yielding time dependent
rates in the dynamics of relaxation and allowing virtual processes of small
virtuality $\propto 1/t$ at long time $t$. These \emph{off-shell} processes
lead to thermalization despite vanishing S-matrix rates. In the case of
threshold divergences we find that a thermal fixed point is approached as
$e^{-\sqrt{t/t^*}}$ with the relaxation time $t^*$ becoming shorter at high
temperature as a consequence of stimulated emission and absorption. In the
infrared case, the thermal fixed point is approached as $e^{-\gamma(t)}$, where
$\gamma(t)$ features a crossover between a $\propto \ln(t)$ and a $\propto t$
behavior for $t \gg 1/T$. The vanishing of the residue and the crossover in
relaxational dynamics in this case is strikingly reminiscent of the
orthogonality catastrophe in heavy impurity systems. The results yield more
general lessons on thermalization via virtual processes.
