Non-positive energy quasidistributions in coherent collision models

We determine the Kirkwood-Dirac quasiprobability (KDQ) distribution associated to the stochastic instances of internal energy variations for the quantum system and environment particles in coherent Markovian collision models. In the case the interactions between the quantum system and the particles do not conserve energy, the KDQ of the non-energy-preserving stochastic work is also derived. These KDQ distributions can account for non-commutativity, and return the unperturbed average values and variances for a generic interaction-time, and generic local initial states of the quantum system and environment particles. Using this nonequilibrium-physics approach, we certify the conditions under which the collision process of the model exhibits quantum traits, and we quantify the rate of energy exchanged by the quantum system by looking at the variance of the KDQ energy distributions. Finally, we propose an experimental test of our results on a superconducting quantum circuit implementing a qubit system, with microwave photons representing the environment particles.