  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.
