Auto-Organized Dissipative Structures and Regularity on Global Attractors: An Onsager–Cheeger–Renormalization Framework
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| Format: | Recurso digital |
| Langue: | anglais |
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2026
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| _version_ | 1866901557658779648 |
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| author | Caffagni, Andrea |
| author_facet | Caffagni, Andrea |
| contents | <p>We propose an axiomatic multiscale framework for dissipative dynamical systems with a<br>global attractor, organized around a single principle:<br>nonnegative Onsager production propagates under coarse-graining.<br>At a fixed observation scale, each interface carries a sum-of-squares Onsager–Prigogine<br>production polynomial, hence matrix/scalar Onsager bounds and a canonical misalignment<br>defect. Eliminating intermediate scales by minimum-production decimation preserves this<br>structure and defines an autonomous renormalization map on shell graphs. Fixed points of<br>this map are precisely configurations that satisfy Prigogine closure at all scales simultaneously.<br>On the same observed graph, the production structure induces a weighted Dirichlet form<br>and a Cheeger-type dichotomy: either the scale–channel graph is coercive (self-averaging and<br>reverse-Hölder improvement) or bottlenecked (flux suppression and tail drainage). Combined<br>with an observationwise entropy-transport package and an explicit modular coercive-closure<br>interface, both branches yield regularity upgrades on the global attractor. At the renormalization<br>level, hyperbolic saddles organize transitions between universality classes: shadow<br>times, parameter accumulation, and finite-size corrections are controlled by the unstable RG<br>eigenvalue δu, while the closed thermodynamic sector carries its own explicit dyadic drift<br>eigenvalue δth = 2.<br>The manuscript is intentionally modular. We state explicit axioms (A0, A0♭, A0♯, A1–<br>A6), prove the abstract implications conditional on those axioms, and separate them from<br>model-dependent verification programs. In particular, no new well-posedness theorem for 3D<br>Navier–Stokes is claimed here. A companion numerical campaign on Sabra and GOY shell<br>models validates several theorem-level diagnostics of the thermodynamic RG (Appendix L)<br>and keeps all phenomenology-level and transition-dynamics items explicitly non-claim.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19910029 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Auto-Organized Dissipative Structures and Regularity on Global Attractors: An Onsager–Cheeger–Renormalization Framework Caffagni, Andrea Mathematical physics dissipative dynamical systems renormalization group Onsager reciprocal relations Cheeger inequality non-equilibrium thermodynamics coarse-graining global attractor Dirichlet form Sabra shell model turbulence theory <p>We propose an axiomatic multiscale framework for dissipative dynamical systems with a<br>global attractor, organized around a single principle:<br>nonnegative Onsager production propagates under coarse-graining.<br>At a fixed observation scale, each interface carries a sum-of-squares Onsager–Prigogine<br>production polynomial, hence matrix/scalar Onsager bounds and a canonical misalignment<br>defect. Eliminating intermediate scales by minimum-production decimation preserves this<br>structure and defines an autonomous renormalization map on shell graphs. Fixed points of<br>this map are precisely configurations that satisfy Prigogine closure at all scales simultaneously.<br>On the same observed graph, the production structure induces a weighted Dirichlet form<br>and a Cheeger-type dichotomy: either the scale–channel graph is coercive (self-averaging and<br>reverse-Hölder improvement) or bottlenecked (flux suppression and tail drainage). Combined<br>with an observationwise entropy-transport package and an explicit modular coercive-closure<br>interface, both branches yield regularity upgrades on the global attractor. At the renormalization<br>level, hyperbolic saddles organize transitions between universality classes: shadow<br>times, parameter accumulation, and finite-size corrections are controlled by the unstable RG<br>eigenvalue δu, while the closed thermodynamic sector carries its own explicit dyadic drift<br>eigenvalue δth = 2.<br>The manuscript is intentionally modular. We state explicit axioms (A0, A0♭, A0♯, A1–<br>A6), prove the abstract implications conditional on those axioms, and separate them from<br>model-dependent verification programs. In particular, no new well-posedness theorem for 3D<br>Navier–Stokes is claimed here. A companion numerical campaign on Sabra and GOY shell<br>models validates several theorem-level diagnostics of the thermodynamic RG (Appendix L)<br>and keeps all phenomenology-level and transition-dynamics items explicitly non-claim.</p> |
| title | Auto-Organized Dissipative Structures and Regularity on Global Attractors: An Onsager–Cheeger–Renormalization Framework |
| topic | Mathematical physics dissipative dynamical systems renormalization group Onsager reciprocal relations Cheeger inequality non-equilibrium thermodynamics coarse-graining global attractor Dirichlet form Sabra shell model turbulence theory |
| url | https://doi.org/10.5281/zenodo.19910029 |