Page-curve-like entropy dynamics in a classical elastic bit lattice

Area of Science:

• Classical Mechanics
• Quantum Information Theory
• Nonlinear Dynamics

Background:

• Quantum systems exhibit phenomena like entanglement entropy, crucial for understanding information flow.
• Classical systems typically do not display such quantum information-theoretic behaviors.
• Nonlinear lattices offer potential platforms for emulating quantum phenomena.

Purpose of the Study:

• To engineer a classical nonlinear lattice that reproduces the "Page curve" of bipartite entanglement entropy.
• To establish a classical analog of quantum entanglement dynamics using mechanical systems.
• To explore the intersection of classical dynamics and information theory.

Main Methods:

• Constructed a lattice of four elastically coupled steel spheres (two dumbbells).
• Used harmonic driving to excite the lattice and a laser-Doppler vibrometer to record velocities.
• Mapped the system's state into a Hilbert space and defined a classical entanglement entropy.

Main Results:

• The classical entanglement entropy exhibited a characteristic rise-and-fall "Page curve", mirroring quantum predictions.
• Observed dynamics were driven by nonlinear mode coupling and tunable via driver parameters.
• The system successfully emulated bipartite entanglement entropy evolution in a classical mechanical analog.

Conclusions:

• Classical nonlinear lattices can reproduce quantum information-theoretic phenomena like the Page curve.
• Tabletop mechanical systems can serve as platforms for studying entanglement-based diagnostics.
• This work provides an accessible avenue for exploring fundamental questions in dynamics and information theory.