  We consider the communication of classical and quantum information between
two arbitrary observers in asymptotically flat spacetimes (possibly containing
black holes) and investigate what is the energy cost for such information
transmission. By means of localized two-level quantum systems, sender and
receiver can use a quantum scalar field as a communication channel. As we have
already shown in a previous paper, such a channel has non-vanishing classical
capacity as well as entanglement-assisted classical and quantum capacities.
Here we will show that the change in the expectation value of the energy of the
system during the communication process can be separated in: (i) a contribution
coming from the particle creation due to the change of the spacetime, (ii) a
contribution associated with the energy needed to switch-on/off each qubit, and
{\bf (iii)} a term which comes from the communication process itself. For the
quantum channel considered here, we show that the extra energy cost needed for
communication vanishes. As a result, if one has already created a system of
qubits for some specific task (e.g., quantum computation) one can also reliably
convey information between its parts with no extra energy cost. We conclude the
paper by illustrating the form of the channel capacities and energy
contributions in two paradigmatic cases in Minkowski spacetime: (1) sender and
receiver in inertial motion and (2) sender in inertial motion while the
receiver is uniformly accelerated.
