The entanglement entropy of a black hole and that of its Hawking radiation are expected to follow the socalled 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-plusbath model has been ...
The entanglement entropy of a black hole and that of its Hawking radiation are expected to follow the socalled 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-plusbath model has been proposed which shows a similar behavior. Here, we make a general argument as to
why such a Page-curve-like entanglement dynamics should be expected to hold generally for system-plusbath models at small coupling and low temperatures, when the system is initialized 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 localized impurity is
higher for more localized initial states. In the second example, for an impurity initialized in the excited
state, the Page time—when the entropy reaches its maximum—occurs when the excitation has half
decayed.