  Master equations are a vital tool to model heat flow through nanoscale
thermodynamic systems. Most practical devices are made up of interacting
sub-system, and are often modelled using either local master equations (LMEs)
or global master equations (GMEs). While the limiting cases in which either the
LME or the GME breaks down are well understood, there exists a 'grey area' in
which both equations capture steady-state heat currents reliably, but predict
very different transient heat flows. In such cases, which one should we trust?
Here, we show that, when it comes to dynamics, the local approach can be more
reliable than the global one for weakly interacting open quantum systems. This
is due to the fact that the secular approximation, which underpins the GME, can
destroy key dynamical features. To illustrate this, we consider a minimal
transport setup and show that its LME displays exceptional points (EPs). These
singularities have been observed in a superconducting-circuit realisation of
the model [1]. However, in stark contrast to experimental evidence, no EPs
appear within the global approach. We then show that the EPs are a feature
built into the Redfield equation, which is more accurate than the LME and the
GME. Finally, we show that the local approach emerges as the weak-interaction
limit of the Redfield equation, and that it entirely avoids the secular
approximation.
