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

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