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

[2605.05604] Temporal Coarse-Graining as the Origin of Macroscopic Friction in Quantum Spin Chains via Data-Driven Liouvillian Extraction Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2605.05604 (quant-ph) [Submitted on 7 May 2026 ( v1 ), last revised 27 Jul 2026 (this version, v2)] Title: Temporal Coarse-Graining as the Origin of Macroscopic Friction in Quantum Spin Chains via Data-Driven Liouvillian Extraction Authors: Seiki Saito View PDF HTML (experimental) Abstract: Understanding how macroscopic irreversible hydrodynamics emerges from the reversible unitary dynamics of isolated quantum many-body systems remains a central challenge. Conventional approaches force spin density dynamics into purely diffusive models, obscuring the interplay of pressure, spin current, and local friction, and leave open the role of the observer's temporal resolution. We introduce a fully data-driven framework based on generalized Extended Dynamic Mode Decomposition (gEDMD) integrated with the Mori-Zwanzig projection. By expanding the observable dictionary to include spin currents, we extract the Navier-Stokes hydrodynamic coefficients from a chaotic XXZ spin chain across temporal coarse-graining scales. Our unconstrained extraction reveals a dichotomy: the mechanical elasticity ($c^2$) derives from the exact unitary dynamics, preserving microscopic reversibility, whereas the macroscopic friction ($\gamma$) and kinematic viscosity ($\nu$) show zero net dissipation, oscillating rapidly around zero in the exact-derivative limit. Genuine macroscopic transport therefore requires finite temporal coarse-graining: at a finite observation timescale ($\Delta t_{cg} > 0$) the system passes through a crossover where these fluctuations average out, establishing an intermediate functional regime with strictly positive friction and viscosity. We further show that the coarse-grained generator is a predictive reduced model requiring only $O(N)$ macroscopic observables, and that the sign of the emergent friction is inherited from the causal, forward-in-time direction of the inference: time-symmetric estimators yield zero net dissipation at any coarse-graining scale. Macroscopic friction in isolated quantum systems is thus not an absolute property but an emergent phenomenon dictated by the temporal resolution and causal direction of the observer's description. Subjects: Quantum Physics (quant-ph) ; Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2605.05604 [quant-ph] (or arXiv:2605.05604v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.05604 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. Research 8, 033348, 22 September, 2026 Related DOI : https://doi.org/10.1103/41m6-x2m9 Focus to learn more DOI(s) linking to related resources Submission history From: Seiki Saito [ view email ] [v1] Thu, 7 May 2026 02:41:56 UTC (6,606 KB) [v2] Mon, 27 Jul 2026 00:36:40 UTC (7,274 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-05 Change to browse by: cond-mat cond-mat.stat-mech References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. 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