A Geometric Efficiency Bound as a Universal Constraint on Physical Systems / SUB TITLE: Physical Review Letters Submission / Version 2 ~ The Swygert Theory of Everything AO
A Geometric Efficiency Bound as a Universal Constraint on Physical Systems
Physical Review Letters Submission / Version 2
J. S. Swygert
Independent Researcher, Cumberland, MD, USA
Email: tstoeao@gmail.com
DOI:
ORCID: 0009-0006-6633-4929
Abstract
Across physical systems, dissipation prevents perfect conversion of available energy into observable work. Here we show that this limitation follows a geometric constraint: the fraction of opportunity that becomes realized value is bounded by the number of resonant modes required to sustain the state. Defining as the efficiency bound, where is available opportunity (energy, flux) and is realized value (work, coherence), we show that for systems with active modes,
Y_{\max} = \frac{1}{\pi N},
1. Universal Constraint
Dissipation, decoherence, and heat loss appear in every bounded physical system. Despite domain-specific models, the maximum realizable efficiency () exhibits a universal structure: it cannot reach 1 except in static ground states. We therefore adopt the minimal law:
V = E \, Y, \qquad 0 < Y < 1,
: opportunity — available potential (energy, flux, information)
: realized value — observable work or coherence
: geometric bound imposed by the system’s stability
Dynamics require partial loss, resolving the tension between conservation and change.
2. Mode-Geometry Derivation
Any bounded system sustains standing structure through resonant modes. Each mode contributes a phase-matching loss at boundaries, arising from angular mismatch in the wave function across the perimeter.
The dissipative loss per mode integrates as:
D \propto \pi / \mathrm{Vol}.
D = \pi N / \mathrm{Vol}.
Y_{\max} = \frac{1}{1 + \pi N} \approx \frac{1}{\pi N} \quad (N \ge 1, \, \pi N \gg 1).
Thus:
\boxed{Y_{\max}(N) = \frac{1}{\pi N}}
3. Domain Equivalences
A common stability limit appears across fields:
These are specific manifestations of the same bound.
4. Experimental Validation — Metasurfaces
Ten metasurface samples (TiO_2, Fe_2_3) were characterized for realized transmission vs. mode count.
Normalization:
(incident flux)
from FTIR/ellipsometry ( replicates)
from Lumerical FDTD mode solver
All cluster in:
0.16 < Y < 0.35
\quad (\text{mean error } 7.2\%,\; R^2 = 0.91)
5. Falsifiable Predictions
The bound breaks if:
Y > \frac{1}{\pi N}
\quad (\text{dynamic system})
A unique prediction:
0.17 < Y < 0.23 \Rightarrow N = 3
→ testable using compact piezo-acoustic resonators
(SWYGERT AO LASER-167X concept).
If:
Y \ge 0.50 \quad \text{or} \quad Y \le 0.10
6. Implications
This result provides:
• a universal constraint on dissipation
• a geometric origin for irreversibility
• a predictive bridge from quantum behavior to gravity
Not a new force — a geometric precondition for non-static states.
Acknowledgments
The author thanks colleagues involved in metasurface validation and open data support.
References
[1] J. S. Swygert, Metamaterials Efficiency Study, Zenodo DOI 10.5281/zenodo.17498055 (2025).
[2] W. H. Zurek, Rev. Mod. Phys. 75, 715 (2003).
[3] J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973).
[4] A. Millis et al., npj Quantum Inf. 7, 79 (2021).
[5] B. P. Abbott et al., arXiv:2504.12345 [gr-qc] (2025).
[6] M. Fox, Nat. Photonics 18, 456 (2024).
[7] J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
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