  Local quantum master equations provide a simple description of interacting
subsystems coupled to different reservoirs. They have been widely used to study
nonequilibrium critical phenomena in open quantum systems. We here investigate
the validity of such a local approach by analyzing a paradigmatic system made
of two harmonic oscillators each in contact with a heat bath. We evaluate the
steady-state mean occupation number for varying temperature differences and
find that local master equations generally fail to reproduce the results of an
exact quantum-Langevin-equation description. We relate this property to the
inability of the local scheme to properly characterize intersystem
correlations, which we quantify with the help of the quantum mutual
information.
