  We address the detailed study of the energy current and its components, heat
and work, in the boundary-driven 1D XXZ quantum model. We carry out the
investigation by considering two different approaches present in the
literature. First, we take the repeated interaction scheme and derive the
expressions for the currents of heat and work, exchanged between system and
baths. Then, we perform the derivation of the energy current by means of a
Lindblad master equation together with a continuity equation, another approach
which is recurrently used. A comparison between the obtained expressions allows
us to show the consistency of both approaches, and, in the latter expression
derived from the Lindblad equation, it allows us to split the energy, which
comes from the baths to the system, into heat and work. The recognition of work
in the process, that is recurrently ignored in studies of transport, enables us
to understand thermodynamical aspects and to solve some imbroglios in the
physics behind the energy current in the XXZ spin chain.
