  This paper investigates the dynamics of current and efficiency in a bosonic
system consisting of a central system interacting with two reservoirs at
different temperatures. We derive a master equation describing the time
evolution of the density matrix of the system, accounting for the interactions
and energy transfer between the components. We quantify the current,
representing the flow of bosons through the system and analyse its dependence
on the system's parameters and temperatures of the thermal reservoirs. In the
steady state regime, we derived an expression for the efficiency of the energy
transfer process. Our analysis show that quantum effects, such as the
dependence on temperature and the quantum correction factor, can significantly
impact energy transfer efficiency. In particular, we observe that at high
temperatures, the efficiency of the quantum system is greater than the Carnot
efficiency. The insights gained from this analysis may have implications in
various fields, including quantum computing and energy harvesting, where
optimising energy utilisation is crucial.
