Universal Energy Fluctuations in Inelastic Scattering Processes

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 Letter, 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 nonunital 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 Letter 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.