Operational Emergence of a Global Phase under Time-Dependent Coupling in Oscillator Networks

[2603.05668] Operational Emergence of a Global Phase under Time-Dependent Coupling in Oscillator Networks Skip to main content Search Submit Donate Log in Condensed Matter > Statistical Mechanics arXiv:2603.05668 (cond-mat) [Submitted on 5 Mar 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Operational Emergence of a Global Phase under Time-Dependent Coupling in Oscillator Networks Authors: Veronica Sanz View PDF HTML (experimental) Abstract: Time-dependent coupling is often interpreted as introducing competition between a protocol rate and an intrinsic synchronization rate. We show that this interpretation is unavailable in the identical, overdamped Kuramoto model when time dependence enters only through a scalar multiplier of a fixed coupling field. The accumulated coupling $S(t)=\int_0^tK(u)\mathrm{d} u$ is then an exact dynamical clock: equal-exposure protocols traverse the same autonomous orbit, and integrable decays produce finite-exposure arrest rather than deterministic loss of adiabatic tracking. This clock suggests a classification under time reparametrization. Deterministic orbit observables and winding sectors are invariant; an additive perturbation $\varepsilon G$ has a leading response that is a linear functional of the reciprocal schedule $w(s)=1/K(t(s))$ against a kernel fixed by the autonomous orbit; and inertia or noncommuting graph generators lie outside this reciprocal-weighted class. Laboratory-time white noise has the corresponding $w$-weighted covariance. We derive exact mode covariances, prove a universal terminal bang--bang optimum under bounded coupling and fixed exposure, and validate both results in nonlinear networks. We also separate information in the full phase sample from information retained by the order parameter. Conditional observation error of $\arg Z$ follows a $1/(NR^2)$ law with a configuration-dependent prefactor, whereas a known-template experiment has Fisher information $N/\sigma^2$ independently of $R$; the efficiency of $\arg Z$ is $R^2/q_2$. Finally, periodic rings exhibit stable winding sectors with strong local but vanishing global order. Comments: 11 pages, 6 figures. Discussion and results improved from v1 Subjects: Statistical Mechanics (cond-mat.stat-mech) ; High Energy Physics - Theory (hep-th); Chaotic Dynamics (nlin.CD); Physics and Society (physics.soc-ph) Cite as: arXiv:2603.05668 [cond-mat.stat-mech] (or arXiv:2603.05668v2 [cond-mat.stat-mech] for this version) https://doi.org/10.48550/arXiv.2603.05668 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Veronica Sanz [ view email ] [v1] Thu, 5 Mar 2026 20:35:20 UTC (101 KB) [v2] Fri, 28 Aug 2026 11:09:32 UTC (124 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.stat-mech < prev | next > new | recent | 2026-03 Change to browse by: cond-mat hep-th nlin nlin.CD physics physics.soc-ph 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? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) 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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