  The construction of the generalized Gibbs ensemble, to which isolated
integrable quantum many-body systems relax after a quantum quench, is based
upon the principle of maximum entropy. In contrast, there are no universal and
model-independent laws that govern the relaxation dynamics and stationary
states of open quantum systems, which are subjected to Markovian drive and
dissipation. Yet, as we show, relaxation of driven-dissipative systems after a
quantum quench can, in fact, be determined by a maximum entropy ensemble, if
the Liouvillian that generates the dynamics of the system has parity-time
symmetry. Focusing on the specific example of a driven-dissipative Kitaev
chain, we show that, similarly to isolated integrable systems, the approach to
a parity-time symmetric generalized Gibbs ensemble becomes manifest in the
relaxation of local observables and the dynamics of subsystem entropies. In
contrast, the directional pumping of fermion parity, which is induced by
nontrivial non-Hermitian topology of the Kitaev chain, represents a phenomenon
that is unique to relaxation dynamics in driven-dissipative systems. Upon
increasing the strength of dissipation, parity-time symmetry is broken at a
finite critical value, which thus constitutes a sharp dynamical transition that
delimits the applicability of the principle of maximum entropy. We show that
these results, which we obtain for the specific example of the Kitaev chain,
apply to broad classes of noninteracting fermionic models, and we discuss their
generalization to a noninteracting bosonic model and an interacting spin chain.
