Scrambling vs. Recurrence: Transition from Integrable to Complex Quantum Dynamics

This paper investigates the emergence of the thermodynamic arrow of time in a closed 8-qubit quantum system. We analyze the tension between information scrambling and Poincaré recurrence by comparing two dynamical regimes: a near-integrable Heisenberg chain (Regime I) and a symmetry-broken chaotic regime (Regime II). Our central numerical result is a collapse of the Poincaré recurrence fidelity from F ≈ 0.99 to F ≈ 0.11 upon introducing symmetry-breaking fields. We provide structural analysis via Krylov subspace growth (Lanczos coefficients), illustrating that irreversibility in finite systems is an emergent property driven by spectral complexity. The global von Neumann entropy remains strictly zero in both regimes, confirming that information is conserved — the apparent irreversibility arises from the complexity of the path by which information returns, not from any fundamental loss. All results are obtained from exact unitary simulation of the Schrödinger equation; no Lindblad or Markov approximations are used. Simulation code: https://zenodo.org/records/18813710