Study of the energy variation in many-body open quantum systems: role of interactions in the weak and strong coupling regimes

We derive an expression for the rate of change of the energy of an interacting many-body system connected to macroscopic leads. We show that the energy variation is the sum of contributions from each different lead. Unlike the charge current each of this contribution can differ from the rate of change of the energy of the lead. We demonstrate that the discrepancy between the two is due to the direct exchange of energy among the considered lead and all other leads. We conclude that the microscopic mechanism behind it are virtual processes via the interacting central region. We also speculate on what are the implications of our findings in the calculation of the thermal conductance of an interacting system.