Black Hole Entropy from Dimensional Information: A First-Principles Derivation

We present a novel derivation of the Bekenstein-Hawking black hole entropy formula using the dimensional information framework. By analyzing event horizons as coherence boundaries with maximal entropy-flow continuity and perfect coherence across the global cut, we demonstrate that the maximum sustainable dimensional information at a black hole horizon scales linearly with its area. Working from thermodynamic coherence constraints at causal boundaries, and without invoking specific microscopic models, we derive the Bekenstein-Hawking entropy scaling as a natural consequence of dimensional information theory, recovering the scaling S_BH = k_B A / (4 ℓ_P^2) as the expected information-theoretic capacity of the horizon. This approach provides a causal-thermodynamic explanation for the area law and situates black hole thermodynamics within a broader framework of dimensional information theory applicable to all causal boundaries in thermodynamically open systems.