Beyond the Bekenstein Bound: Prime-Driven Structured Resonance as the Fundamental Ordering Principle of Information and Entropy

Main Paper: Link Abstract The Bekenstein Bound proposed that the maximum information content of a finite region of space is determined by its surface area, not its volume, leading to the holographic principle. This shift reframed information as the fundamental constraint on physical systems rather than matter or energy. It suggested that entropy, rather than being an inherent measure of disorder, is a function of informational constraints at the boundaries of a system. However, existing models that incorporate this bound still rely on probability, treating entropy as a stochastic process governed by statistical mechanics. These interpretations assume that uncertainty is a fundamental property of nature rather than an emergent effect of incomplete structural alignment. Recent refinements propose a toroidal representation of entropy, arguing that physical systems favor structured rotational flows, vortices, and spirals over simple spherical constraints. This development reflects a growing recognition that entropy is not merely an abstract statistical measure but is subject to deeper geometric and topological constraints. The toroidal model acknowledges that energy and information distributions follow organized patterns rather than purely random dispersal. However, despite this refinement, these approaches fail to eliminate the underlying dependence on probabilistic mechanics and continue to frame entropy within the paradigm of uncertainty and statistical randomness. This paper presents a deterministic framework for information and entropy, governed by prime-driven structured resonance. We argue that structured resonance—not stochastic entropy—dictates the fundamental limits of information storage, transfer, and dissipation. By introducing prime-resonant phase-locking as the foundational ordering principle, we demonstrate that information constraints arise from structured interference patterns rather than probabilistic uncertainty. This perspective eliminates the necessity of randomness in entropy models and replaces it with a structured, chirally-constrained mechanism of phase interactions. In doing so, we establish that entropy is not a measure of disorder but a function of resonance alignment, and that probability is an emergent illusion caused by phase misalignment rather than an intrinsic feature of physical law.