Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Recurso digital |
| Sprache: | |
| Veröffentlicht: |
Zenodo
2026
|
| Schlagworte: | |
| Online-Zugang: | https://doi.org/10.5281/zenodo.20208935 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Inhaltsangabe:
- <p class="p1">This technical note introduces a conservative scalar diagnostic for comparing compactness, entropy saturation, coupling organization, and density-like structure in gravitational systems. The construction uses the constrained binary partition <span class="s1">a+b=1</span> and associated Thales variables <span class="s1">h=\sqrt{ab}</span>, <span class="s1">\chi=|a-b|</span>, and <span class="s1">R_{\rm part}=1/(4ab)</span> to measure departure from balanced coupling.</p> <p class="p1">The main physical motivation is Padmanabhan’s equipartition view of gravitational dynamics. The note does not derive or replace the Einstein field equation, nor does it claim to prove thermodynamic gravity. Instead, it provides a normalized scalar language for identifying how far a system lies from two-channel equipartition once physically meaningful channels are defined.</p> <p class="p1">For compact gravitating systems, the compactness parameter <span class="s1">C=2GM/(rc^2)</span> is read as the partition <span class="s1">C+(1-C)=1</span>. Using standard formulas, the note records the exact identities <span class="s1">S_B/S_{BH}=C</span>, <span class="s1">T_{\rm screen}/T_H=C</span>, and <span class="s1">T_{\rm prop}/T_H=C/\sqrt{1-C}</span>, while carefully distinguishing the physical Schwarzschild horizon response <span class="s1">R_H=(1-C)^{-1}</span> from the symmetric partition response <span class="s1">R_{\rm part}=[4C(1-C)]^{-1}</span>.</p> <p class="p1">The note also separates ordinary material density, coupling density, and rational-state density, arguing that material concentration and coupling organization should not be conflated. A pilot cosmic-web local-mode analysis based on the SDSS-IV Cosmic Web Catalog finds that local gradient partitions are dominated by near-equipartition states, while higher-<span class="s1">R</span> regimes show weaker balanced gradient participation and mildly higher ordinary density. This supports the use of <span class="s1">R_{\rm part}</span> as a diagnostic coordinate for entropy-like organization, while leaving physical interpretation to domain-specific gravitational theory.</p>