  A theory is developed for the evolution of the non-equilibrium distribution
of quasiparticles when the scattering rate decreases due to particle
collisions. We propose a "modified one-collision approximation" which is most
effective for high-energy quasiparticle distributions. This method is used to
explain novel measurements of the non-monotonic energy dependence of the signal
of scattered electrons in a 2D system. The observed effect is related to a
crossover from the ballistic to the hydrodynamic regime of electron flow.
