Energy statistics in quantum scattering theory.

We show that the energy statistics of a quantum system can be probed by a collision with a moving particle. In this setup, the particle acts both as an external drive and as an energy measurement device for the system. At high kinetic energies, the resulting energy statistics is the same as the work distribution resulting from the two-point measurement scheme applied to a closed system in a thermal state, from which the usual work fluctuation relations and second law of thermodynamics follow. At low kinetic energies, the energy statistics is radically modified by closed scattering channels which favor de-excitation processes in the system, leading to modified work fluctuation relations. Nevertheless, the second law of thermodynamics still holds, where an extra term captures the information about the scattering matrix at low kinetic energies. Our results show that energy fluctuations can be defined within an autonomous and realistic setting, where both the probe and the system to be probed are treated as quantum systems in their own right.