Understanding the emergence of macroscopic irreversible hydrodynamics from the reversible unitary dynamics of isolated quantum many-body systems remains a fundamental challenge. Conventional approaches often force spin density dynamics into purely diffusive models, obscuring the microscopic interplay of pressure, spin current, and local friction. Furthermore, reconciling true irreversibility with strictly unitary evolution raises fundamental questions about the role of the observer's temporal resolution. In this paper, we introduce a fully data-driven framework based on generalized extended dynamic mode decomposition integrated with the Mori-Zwanzig projection. By expanding the observable dictionary to explicitly include spin currents, we directly extract the Navier-Stokes hydrodynamic coefficients from a chaotic XXZ spin chain across varying temporal coarse-graining scales. Our unconstrained extraction reveals a clear physical dichotomy: The mechanical elasticity $\left(c^2\right)$ is intrinsically derived from the exact unitary dynamics, preserving strict microscopic reversibility. In contrast, the macroscopic friction $\left(\gamma \right)$ and kinematic viscosity $\left(\nu \right)$ exhibit zero net dissipation, oscillating rapidly around zero in the exact-derivative limit. We demonstrate that genuine macroscopic transport cannot be established without finite temporal coarse graining. By introducing a finite observation timescale $(\mathrm{\Delta }{t}_{\mathrm{cg}}>0)$, the system passes through a distinct crossover timescale where these reversible fluctuations average out, establishing an intermediate functional regime that yields strictly positive friction and viscosity. We further show that the coarse-grained generator constitutes a predictive reduced model requiring only $O\left(N\right)$ macroscopic observables, and that the sign of the emergent friction is inherited from the causal, forward-in-time direction of the coarse-grained inference: Time-symmetric estimators yield zero net dissipation at any coarse-graining scale. Our results demonstrate that macroscopic friction in isolated quantum systems is not an absolute property, but an emergent phenomenon dictated by the temporal resolution and the causal direction of the observer's coarse-grained description.

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• Eigenstate thermalization
• Open quantum systems & decoherence
• Quantum coherence & coherence measures
• Quantum many-body systems
• Data analysis
• Hydrodynamics
• Machine learning
• Quantum spin chains