Exactly solvable model of calorimetric measurements

Calorimetric measurements are experimentally realizable methods to assess thermodynamics relations in quantum devices. With this motivation in mind, we consider a resonant level coupled to a Fermion reservoir. We consider transient process, in which the interaction between the level and the reservoir is initially switched on and then switched off again. We find the time dependence of the energy of the reservoir, of the energy of the level and of the interaction energy between them at weak, intermediate, strong and ultra-strong coupling. We also determine the statistical distributions of these energies.