Solid lines show the distribution of leptons formed at three epochs (10 s, 100 s, 1 ks—colored lines) and total distribution at 2 ks (black), integrated over the indicated source evolution and without radiative cooling (b = 0). The quasi-instantaneous distributions are normalized to that integrated up to 2 ks. The source GeV fluence is constant, its deceleration ﹩{\Gamma }(t)﹩ and break energy ﹩{{\varepsilon }_{b}}﹩ evolutions correspond to a blast-wave interacting with a wind-like external medium. Black lines show time-integrated (up to 2 ks) lepton distribution with synchrotron and inverse-Compton cooling, for different fractions b of the post-shock energy that is in the magnetic field. The cooled lepton distributions display a break at the energy for which leptons lose half of their energy over a dynamical timescale. Above the break, the lepton distribution slope increases by unity (right panel). The higher the magnetic field parameter b, the lower the lepton cooling-break energy.