I will discuss a simple model of a non-equilibrium quantum network whose dynamics can be expressed and exactly solved in terms of a time-local master equation. Specifically, the model comprises a pair of coupled fermionic modes, each one locally exchanging energy and particles with an independent, macroscopic thermal reservoir. We will find that the generator of the asymptotic master equation is not additive, i.e. it cannot be expressed as a sum of contributions describing the action of each reservoir alone. Instead, an additional interference term arises, which generates coherence in the energy eigenbasis of the open system. This coherence is associated with the current of conserved particles flowing in the steady state. Notably, non-additivity arises even for wide-band reservoirs coupled arbitrarily weakly to the system. These results shed light on the non-trivial interplay between multiple thermal noise sources in modular open quantum systems.