An energetic parton crossing a hot or dense quark-gluon plasma (QGP) can lose energy through elastic collisions with the medium, a process contributing to jet and hadron suppression observed in heavy-ion and recently also in light-ion collisions. Going beyond existing approaches, which mostly focus on the average energy loss per unit distance for large systems, we derive the full energy loss probability distribution (or quenching weight) from first principles using Landau’s kinetic equation to resum the energy losses suffered in
multiple successive elastic scatterings. The distribution captures rare but significant fluctuations, arising from the long tail of the single scattering spectrum, and includes the possibility of energy gain from the medium, both effects being especially relevant for small
systems. Our results fill a conceptual gap in the modelling of jet/hadron and heavy flavour suppression, where usually only those fluctuations of the radiative energy loss are taken into account, and may help interpret high-multiplicity pp and pA data.