Observable modal leakage in coarse-grained stochastic dynamics: a geometric identity and its physical consequences
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| Sprache: | Englisch |
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2026
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| _version_ | 1866901824570654720 |
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| author | Muñoz Vicedo, Sergio José |
| author_facet | Muñoz Vicedo, Sergio José |
| contents | <p>This work establishes an exact geometric identity governing observable relaxation in reversible stochastic dynamics.</p> <p>For any centered observable and the leading nontrivial eigenfunction of a self adjoint Markov operator, the normalized leading modal weight is equal to the squared cosine of the angle between them. The complementary modal leakage is equal to the squared sine of the same angle.</p> <p>The manuscript shows that effective one dimensional relaxation is controlled not by the spectral envelope of the transfer operator, but by the geometric alignment between measured observables and leading relaxation modes.</p> <p>The theory is developed for Gaussian autoregressive and Ornstein Uhlenbeck processes using total positivity, Gantmacher Krein oscillation theory, and Hermite spectral representations. Numerical verification is provided across synthetic systems and coarse grained physical pipelines, including GW150914 ringdown data and neural population surrogate dynamics.</p> <p>The manuscript further shows that large fitted spectral envelopes may arise as coarse graining artifacts and do not by themselves characterize observable relaxation dynamics.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20178586 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Observable modal leakage in coarse-grained stochastic dynamics: a geometric identity and its physical consequences Muñoz Vicedo, Sergio José Markov operators stochastic dynamics spectral theory transfer operators coarse graining Gantmacher-Krein total positivity Ornstein-Uhlenbeck AR(1) modal decomposition observable geometry <p>This work establishes an exact geometric identity governing observable relaxation in reversible stochastic dynamics.</p> <p>For any centered observable and the leading nontrivial eigenfunction of a self adjoint Markov operator, the normalized leading modal weight is equal to the squared cosine of the angle between them. The complementary modal leakage is equal to the squared sine of the same angle.</p> <p>The manuscript shows that effective one dimensional relaxation is controlled not by the spectral envelope of the transfer operator, but by the geometric alignment between measured observables and leading relaxation modes.</p> <p>The theory is developed for Gaussian autoregressive and Ornstein Uhlenbeck processes using total positivity, Gantmacher Krein oscillation theory, and Hermite spectral representations. Numerical verification is provided across synthetic systems and coarse grained physical pipelines, including GW150914 ringdown data and neural population surrogate dynamics.</p> <p>The manuscript further shows that large fitted spectral envelopes may arise as coarse graining artifacts and do not by themselves characterize observable relaxation dynamics.</p> |
| title | Observable modal leakage in coarse-grained stochastic dynamics: a geometric identity and its physical consequences |
| topic | Markov operators stochastic dynamics spectral theory transfer operators coarse graining Gantmacher-Krein total positivity Ornstein-Uhlenbeck AR(1) modal decomposition observable geometry |
| url | https://doi.org/10.5281/zenodo.20178586 |