The Relational Arrow of Time: Coherence, Asymmetry, and Temporal Directionality in the RTLI Framework

This note introduces a relational perspective on the arrow of time based on the Relational Threshold and Layered Index (RTLI) framework. RTLI identifies a universal coherence parameter, λ, which spans a narrow corridor between the quantum threshold \sqrt{e} \approx 1.649 and the geometric critical value 7/4 = 1.75. Quantum systems tend to evolve toward reduced relational structure (decoherence), while geometric systems evolve toward increased relational order (structure formation). These two tendencies define dual arrows of time that coexist within the coherence corridor. Using cosmological and galactic dynamics evidence—especially the observed value \lambda \approx 1.70 at recombination and in SPARC galactic data—the work argues that our universe resides in the geometric-dominated region of this corridor. This naturally explains why macroscopic systems exhibit a strong time direction aligned with increasing structure and thermodynamic irreversibility. RTLI reframes entropy not as a universal scalar law but as a regime-dependent projection of deeper relational asymmetry. Quantum entropy, thermodynamic entropy, and gravitational structure are all manifestations of the same underlying flow of coherence. This approach provides a unified conceptual framework linking decoherence, thermodynamics, and cosmological evolution, while offering a relational basis for the emergence of temporal directionality.