  There is a current interest in quantum thermodynamics in the context of open
quantum systems. An important issue is the consistency of quantum
thermodynamics, in particular the second law of thermodynamics, i.e., the flow
of heat from a hot reservoir to a cold reservoir. Here recent emphasis has been
on composite system and in particular the issue regarding the application of
local or global master equations. In order to contribute to this discussion we
discuss two cases, namely as an example a single qubit and as a simple
composite system two coupled qubits driven by two heat reservoirs at different
temperatures, respectively. Applying a global Lindblad master equation approach
we present explicit expressions for the heat currents in agreement with the
second law of thermodynamics. The analysis is carried out in the Born-Markov
approximation. We also discuss issues regarding the possible presence of
coherences in the steady state.
