  A three-terminal device, able to control the heat currents flowing through
it, is known as a quantum thermal transistor whenever it amplifies two output
currents as a response to the external source acting on its third terminal.
Several efforts have been proposed in the direction of addressing different
engineering options of the configuration of the system. Here, we adhere to the
scheme in which such a device is implemented as a three-qubit system that
interacts with three separate thermal baths. However, another interesting
direction is how to engineer the thermal reservoirs to magnify the current
amplification. Here, we derive a quantum dynamical equation for the evolution
of the system to study the role of distinct dissipative thermal noises. We
compare the amplification gain in different configurations and analyze the role
of the correlations in a system exhibiting the thermal transistor effect, via
measures borrowed from the quantum information theory.
