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Auteur principal:	De Jesus, Elias
Format:	Recurso digital
Langue:
Publié:	Zenodo 2025
Sujets:	• Relational Thermodynamic Layered Index (RTLI) • Information Geometry • Fisher Metric • Shannon Entropy • Directional Entropy • Coherence Corridor • Geometric Information Theory • Thermodynamic Slow-Roll • Coherence Amplitude • Strong CP Problem • Cosmology • CMB Low-ℓ Anomalies • Geometric Phase Space • Riemannian Measure • Statistical Physics
Accès en ligne:	https://doi.org/10.5281/zenodo.17824703
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This work develops the information-geometric foundations of the Relational Thermodynamic Layered Index (RTLI), showing that coherence is not merely a dynamical effect but a geometric property of parameter space itself. By endowing the interval [\lambda_{\mathrm{IR}}, \lambda_{\mathrm{UV}}]—the RTLI coherence corridor—with a Fisher information metric, we obtain a natural Riemannian volume measure that reshapes the meaning of entropy. This leads to a geometrically corrected entropy functional S_\lambda = H + \ln A(\lambda), \qquad A(\lambda) = (\lambda - \lambda_{\mathrm{IR}})(\lambda_{\mathrm{UV}} - \lambda), where the additional term \mathbf{\ln A(\lambda)} is not an assumption and not a heuristic correction. Instead, it emerges uniquely from the underlying geometry, making it the only entropy form consistent with the Riemannian structure of the coherence manifold. A further conceptual breakthrough arises from the slow-roll evolution of \lambda(t). Because the coherence amplitude A(\lambda) is asymmetric around its saddle point, the entropy acquires a directional drift: frac{dS_\lambda}{dt} = -2b(\lambda - \lambda_c), where \lambda_c is the midpoint (saddle) of the corridor potential V(\lambda) = -\ln A(\lambda). This establishes a new kind of informational arrow—a geometric arrow of information—that operates even in fully reversible thermodynamic conditions. In other words, directionality becomes a property of geometry, not disorder. Finally, this framework yields concrete, cross-disciplinary predictions. The geometric suppression encoded in A(\lambda) offers a natural avenue toward explaining the strong CP problem, contributes to understanding low-\ell CMB anomalies, and introduces coherence-sensitive corrections to quantum information measures. Taken together, this work provides the first explicit information-geometric formulation of RTLI and positions the coherence corridor as a unifying geometric structure with testable physical consequences across multiple domains of physics.

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