Directional Information Theory from Geometric Coherence: The RTLI Framework
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2025
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| _version_ | 1866902002638782464 |
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| author | De Jesus, Elias |
| author_facet | De Jesus, Elias |
| contents | <p><strong>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.</strong><span> By endowing the interval </span><span>[\lambda_{\mathrm{IR}}, \lambda_{\mathrm{UV}}]</span><span>—the RTLI coherence corridor—with a </span><strong>Fisher information metric</strong><span>, we obtain a natural Riemannian volume measure that reshapes the meaning of entropy. This leads to a </span><strong>geometrically corrected entropy functional</strong></p> <p><span>S_\lambda = H + \ln A(\lambda), \qquad A(\lambda) = (\lambda - \lambda_{\mathrm{IR}})(\lambda_{\mathrm{UV}} - \lambda),</span></p> <p>where the additional term <span>\mathbf{\ln A(\lambda)}</span> is <span><strong>not an assumption</strong></span> and <span><strong>not a heuristic correction</strong></span>. Instead, it <span><strong>emerges uniquely from the underlying geometry</strong></span>, making it the only entropy form consistent with the Riemannian structure of the coherence manifold.</p> <p><span><strong>A further conceptual breakthrough</strong></span> arises from the slow-roll evolution of <span>\lambda(t)</span>. Because the coherence amplitude <span>A(\lambda)</span> is asymmetric around its saddle point, the entropy acquires a <span><strong>directional drift</strong></span>:</p> <p><span>frac{dS_\lambda}{dt} = -2b(\lambda - \lambda_c),</span></p> <p>where <span>\lambda_c</span> is the midpoint (saddle) of the corridor potential <span>V(\lambda) = -\ln A(\lambda)</span>. This establishes a <span><strong>new kind of informational arrow</strong></span>—a <span><strong>geometric arrow of information</strong></span>—that operates even in fully reversible thermodynamic conditions. In other words, <span><strong>directionality becomes a property of geometry, not disorder.</strong></span></p> <p>Finally, this framework yields <span><strong>concrete, cross-disciplinary predictions</strong></span>. The geometric suppression encoded in <span>A(\lambda)</span> offers a natural avenue toward explaining the <span><strong>strong CP problem</strong></span>, contributes to understanding <span><strong>low-</strong></span><span>\ell</span><span><strong> CMB anomalies</strong></span>, and introduces coherence-sensitive corrections to <span><strong>quantum information measures</strong></span>.</p> <p><strong>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.</strong></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17824703 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | Directional Information Theory from Geometric Coherence: The RTLI Framework De Jesus, Elias • 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 <p><strong>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.</strong><span> By endowing the interval </span><span>[\lambda_{\mathrm{IR}}, \lambda_{\mathrm{UV}}]</span><span>—the RTLI coherence corridor—with a </span><strong>Fisher information metric</strong><span>, we obtain a natural Riemannian volume measure that reshapes the meaning of entropy. This leads to a </span><strong>geometrically corrected entropy functional</strong></p> <p><span>S_\lambda = H + \ln A(\lambda), \qquad A(\lambda) = (\lambda - \lambda_{\mathrm{IR}})(\lambda_{\mathrm{UV}} - \lambda),</span></p> <p>where the additional term <span>\mathbf{\ln A(\lambda)}</span> is <span><strong>not an assumption</strong></span> and <span><strong>not a heuristic correction</strong></span>. Instead, it <span><strong>emerges uniquely from the underlying geometry</strong></span>, making it the only entropy form consistent with the Riemannian structure of the coherence manifold.</p> <p><span><strong>A further conceptual breakthrough</strong></span> arises from the slow-roll evolution of <span>\lambda(t)</span>. Because the coherence amplitude <span>A(\lambda)</span> is asymmetric around its saddle point, the entropy acquires a <span><strong>directional drift</strong></span>:</p> <p><span>frac{dS_\lambda}{dt} = -2b(\lambda - \lambda_c),</span></p> <p>where <span>\lambda_c</span> is the midpoint (saddle) of the corridor potential <span>V(\lambda) = -\ln A(\lambda)</span>. This establishes a <span><strong>new kind of informational arrow</strong></span>—a <span><strong>geometric arrow of information</strong></span>—that operates even in fully reversible thermodynamic conditions. In other words, <span><strong>directionality becomes a property of geometry, not disorder.</strong></span></p> <p>Finally, this framework yields <span><strong>concrete, cross-disciplinary predictions</strong></span>. The geometric suppression encoded in <span>A(\lambda)</span> offers a natural avenue toward explaining the <span><strong>strong CP problem</strong></span>, contributes to understanding <span><strong>low-</strong></span><span>\ell</span><span><strong> CMB anomalies</strong></span>, and introduces coherence-sensitive corrections to <span><strong>quantum information measures</strong></span>.</p> <p><strong>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.</strong></p> |
| title | Directional Information Theory from Geometric Coherence: The RTLI Framework |
| topic | • 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 |
| url | https://doi.org/10.5281/zenodo.17824703 |