Page Curve of average subsystem entropy

The Page curve is a curve of average subsystem entropy as a function of subsystem size. The curve starts from 0, rises, peaks near the maximal possible entropy when the subsystem makes up half of the total system, and then falls back to 0. We here describe subsystem entropy, averaging over quantum states, and why the curve rises and falls in that manner. We also discuss the connection between the curve and the black hole information paradox.