A useful relationship between time-dependent and steady state solutions of the Boltzmann equation

A simple proof shows that, under certain conditions, a solution of the time-dependent Boltzmann equation integrated over the lifetime of a finite event equals the steady state solution. This is true regardless of the shape of the particle injection function. A key restriction is that the transport parameters remain constant in time on the flux tube or set of flux tubes where the measurements are made, a condition most likely to be satisfied in short-duration events. The theorem has important practical benefits: it means that steady state analysis techniques can be applied with rigor to certain solar particle events, and at the same time it permits improved statistical accuracy by summing measurements over the whole event.