Time-Dependent Entropy of Entanglement as a Classical Analogue of the Page Curve

We explore whether a minimal, purely classical mechanical system can reproduce one of the hallmark signatures of quantum and black-hole physics, the Page Curve. In black holes, this curve represents how information seems to disappear as matter falls in, then reappears as the black hole evaporates. We demonstrate that a similar information-flow pattern can emerge from a purely classical mechanical system. Our system consists of two epoxy-bonded "granular dumbbells" placed side-by-side and coupled through Hertzian contact. Each dumbbell acts like an elastic bit, a classical version of a qubit, with its own normal modes. A piezoelectric transducer harmonically drives one end of the assembly while the opposite end remains fixed, and a laser-Doppler vibrometer records and measures the motion of each sphere. Nonlinear coupling between these dumbbells causes their vibrations to mix and exchange energy and phases that form complex behaviors from mass interactions. Measurements taken suggest the subsystems within these composite, granular networks reflect time-based entropy of entanglement, the measure for information flow in interacting many-body systems and the diagnostic that underpins Hawking's celebrated Page curve for unitary black-hole evaporation. From our observations and entropy calculations, this behavior appears as a cyclic rise and fall, closely matching the Page curve and black-hole information recovery. The amplitude and timing of these entropy cycles depend on the driving frequency, amplitude, and contact geometry. By capturing the full motion of every sphere, this system provides a fully measurable, decoherence-free platform for studying how information scrambles and later re-emerges. The experiment bridges nonlinear dynamics, quantum information theory, and black-hole physics, showing that fundamental information-flow behavior can arise from purely classical mechanics. This simple yet powerful model offers both a new research tool and an intuitive, hands-on way to visualize the physics behind the Page curve.