  The discontinuity, or imaginary part of a self-energy at finite temperature
is proportional to the rate at which the corresponding particles are produced
when very few of them are present, and also to the rate at which their phase
space density approaches the thermal one. These relations were suggested by
Weldon [1], who demonstrated them for low orders in perturbation theory. Here
we show that they are valid at leading order in a linear coupling of the
produced particles, and to all orders in all other interactions of the hot
plasma, if there is a separation of the time scales for the production and for
the thermalization of the bulk of the plasma.
