  The entanglement entropy of a black hole, and that of its Hawking radiation,
are expected to follow the so-called Page curve: After an increase in line with
Hawking's calculation, it is expected to decrease back to zero once the black
hole has fully evaporated, as demanded by unitarity. Recently, a simple
system-plus-bath model has been proposed which shows a similar behaviour. Here,
we make a general argument as to why such a Page-curve-like entanglement
dynamics should be expected to hold generally for system-plus-bath models at
small coupling and low temperatures, when the system is initialised in a pure
state far from equilibrium. The interaction with the bath will then generate
entanglement entropy, but it eventually has to decrease to the value prescribed
by the corresponding mean-force Gibbs state. Under those conditions, it is
close to the system ground state. We illustrate this on two paradigmatic
open-quantum-system models, the exactly solvable harmonic quantum Brownian
motion and the spin-boson model, which we study numerically. In the first
example we find that the intermediate entropy of an initially localised
impurity is higher for more localised initial states. In the second example,
for an impurity initialised in the excited state, the Page time--when the
entropy reaches its maximum--occurs when the excitation has half decayed.
