  A nearly-integrable isolated quantum many-body system reaches a
quasi-stationary prethermal state before a late thermalization. Here, we
revisit a particular example in the settings of an open quantum system. We
consider a collection of non-interacting atoms coupled to a spatially
correlated bosonic bath characterized by a bath correlation length. Our result
implies that the integrability of the system depends on such a correlation
length. If this length is much larger than the distance between the atoms, such
a system behaves as a nearly integrable open quantum system. We study the
properties of the emerging prethermal state for this case, i.e., the state's
lifetime, the extensive numbers of existing quasi-conserved quantities, the
emergence of the generalized Gibbs state, and the scaling of von Neumann
entropy, etc. We find that for the prethermal state, the maximum growth of
entropy is logarithmic with the number of atoms, whereas such growth is linear
for the final steady state, which is the Gibbs state in this case. Finally, we
discuss how such prethermal states can have significant applications in quantum
entanglement storage devices.
