Supplementary Video for "Temporal Coarse-Graining as the Origin of Macroscopic Friction in Quantum Spin Chains via Data-Driven Liouvillian Extraction"

Supplementary Videos for "Temporal Coarse-Graining as the Origin of Macroscopic Friction in Quantum Spin Chains via Data-Driven Liouvillian Extraction" This repository contains the supplementary animations visualizing the dynamic evolution of Liouvillian spectra and emergent hydrodynamic coefficients in isolated chaotic XXZ spin chains. The data was extracted using a fully data-driven framework based on generalized Extended Dynamic Mode Decomposition (gEDMD) integrated with the Mori-Zwanzig projection. These animations provide direct visual evidence of the physical crossover from strict microscopic reversibility to emergent macroscopic dissipation, driven by the observer's temporal resolution. File Descriptions: Sup.1_q8_Liouvillian_Dynamics.gifVisualizes the Liouvillian spectrum evolution in an isolated 8-qubit system. It contrasts the strictly reversible dynamics captured by the complete observable basis (Dict B, remaining on the imaginary axis) against the apparent dissipation and quantum echoes (eigenvalues scattering across the complex plane) that emerge when projecting onto a restricted macroscopic dictionary (Dict A). Sup.2_q8_contact_Liouvillian_Dynamics.gifDemonstrates the genesis of decoherence through a system-environment quench protocol in the 8-qubit system. It compares the exact dynamics of the full universe ("Laplace's Demon") with the restricted target system (Dict S), illustrating how eigenvalues permanently scatter across the complex plane after contact, visualizing the rapid loss of local information to the bath. Sup.3_q20_Liouvillian_Dynamics.gifTracks the complex plane spectra in a partitioned 20-qubit system. It highlights the distinct dynamical roles of the target system (Dict S, localized dissipation), the macroscopic pointer mediating bidirectional information flow (Dict L, wide spectral spread), and the environment energy (Dict E, intermittent energy sloshing). Sup.4_q20_Liouvillian_Dynamics_Exact.gifShows the spatial profiles of the emergent hydrodynamic coefficients ($c^2, \gamma, \nu, D$) in the 20-qubit system evaluated using the exact continuous time derivative. It confirms that without temporal coarse-graining, the local friction $\gamma$ and kinematic viscosity $\nu$ exhibit rapid, reversible fluctuations around zero, yielding no net macroscopic dissipation. Sup.5_q20_Liouvillian_Dynamics_CG.gifShows the identical spatial profiles evaluated under temporal coarse-graining ($\Delta t_{cg} = 0.04$). It visually demonstrates the physical crossover where reversible fluctuations are effectively blurred, establishing an intermediate functional regime with a stable, uniformly positive macroscopic friction $\gamma$ and a consistent macroscopic diffusion $D$.