  We consider a quantum system strongly coupled to multiple heat baths at
different temperatures. Quantum heat transport phenomena in this system are
investigated using two definitions of the heat current, one in terms of the
system energy, and the other in terms of the bath energy. When we consider
correlations among system-bath interactions (CASBI) -- which have a purely
quantum mechanical origin -- the definition in terms of the bath energy becomes
different. We found that CASBI are necessary to maintain the consistency of the
heat current with thermodynamic laws in the case of strong system-bath
coupling. However, within the context of the quantum master equation approach,
both of these definitions are identical. Through a numerical investigation, we
demonstrate this point for a non-equilibrium spin-boson model and a three-level
heat engine model using the reduced hierarchal equations of motion approach
under strongly coupled and non-Markovian conditions. We observe cyclic behavior
of the heat currents and the work performed by the heat engine,and we find that
their phases depend on the system-bath coupling strength. Through consideration
of the bath heat current, we show that the efficiency of the heat engine
decreases as the strength of the system-bath coupling increases, due to the
CASBI contribution. In the case of a large system-bath coupling, the efficiency
increases further if the bath temperature is decreased, with fixed the ratio of
the bath temperatures, due to the discretized nature of energy eigenstates.
This is also considered to be a unique feature of quantum heat engines.
