  Quantum scattering is used ubiquitously in both experimental and theoretical
physics across a wide range of disciplines, from high-energy physics to
mesoscopic physics. In this work, we uncover universal relations for the energy
fluctuations of a quantum system scattering inelastically with a particle at
arbitrary kinetic energies. In particular, we prove a fluctuation relation
describing an asymmetry between energy absorbing and releasing processes which
relies on the non-unital nature of the underlying quantum map. This allows us
to derive a bound on the average energy exchanged. We find that energy
releasing processes are dominant when the kinetic energy of the particle is
comparable to the system energies, but are forbidden at very high kinetic
energies where well known fluctuation relations are recovered. Our work
provides a unified view of energy fluctuations when the source driving the
system is not macroscopic but rather an auxiliary quantum particle in a
scattering process.
