  Threshold and infrared divergences are studied as possible mechanisms of
particle production and compared to the usual decay process in a model quantum
field theory from which generalizations are obtained. A spectral representation
of the propagator of the decaying particle suggests that decay, threshold and
infrared singularities while seemingly different phenomena are qualitatively
related. We implement a non-perturbative dynamical resummation method to study
the time evolution of an initial state. It is manifestly unitary and yields the
asymptotic state and the distribution function of produced particles. Whereas
the survival probability in a decay process falls off as $e^{-\Gamma t}$, for
threshold and infrared divergent cases falls off instead as $e^{-\sqrt{t/t^*}}$
and $t^{-\Delta}$ respectively, with $\Gamma, \Delta \propto (coupling)^2$
whereas $1/t^* \propto (coupling)^4$. Despite the different decay dynamics, the
asymptotic state is qualitatively similar: a kinematically entangled state of
the daughter particles with a distribution function which fulfills the
unitarity condition and is strongly peaked at energy conserving transitions but
broadened by the "lifetime" $1/\Gamma~;~ t^*$ for usual decay and threshold
singularity, whereas it scales with the anomalous dimension $\Delta$ for the
infrared singular case. Threshold and infrared instabilities are production
mechanisms just as efficient as particle decay. If one of the particles is in a
dark sector and not observed, the loss of information yields an entanglement
entropy determined by the distribution functions and increases upon unitary
time evolution.
