  We study the dynamics of correlations in a paradigmatic setup to observe
$\mathcal{PT}$-symmetric physics: a pair of coupled oscillators, one subject to
a gain one to a loss. Starting from a coherent state, quantum correlations
(QCs) are created, despite the system being driven only incoherently, and can
survive indefinitely. $\mathcal{PT}$ symmetry breaking is accompanied by
non-zero stationary QCs. We link $\mathcal{PT}$ symmetry breaking to the
long-time behavior of both total and QCs, which display different scalings in
the $\mathcal{PT}$-broken/unbroken phase and at the exceptional point (EP).
This is analytically shown and quantitatively explained in terms of entropy
balance. The EP in particular stands out as the most classical configuration.
