Narrative Entropy (Sn) and Shannon Entropy (H): A Formal Comparison — From Information Theory to Narrative Physics

Claude Shannon's 1948 entropy formula H = −Σ pᵢ log pᵢ established the mathematical foundation of information theory, quantifying uncertainty in discrete symbol distributions within communication channels. This paper introduces Narrative Entropy (Sn), a formally distinct but epistemologically related metric developed within the Bulut Doctrine framework, which measures the dynamic accumulation of cognitive resistance and structural uncertainty across the temporal dimension of narrative experience. We demonstrate that while Sn draws its foundational intuition from Shannon's H, the two metrics differ across six critical dimensions: domain, temporal structure, measurement object, operational unit, directionality, and engineering function. Sn is not an application of Shannon entropy to literature — it is a structurally independent metric that addresses phenomena Shannon's framework was not designed to capture. We further demonstrate the relationship between Sn, Narrative Gravity (Ng), and biophysical reader output, and provide benchmark calculations for Crime and Punishment, Moby Dick, and Pulp Fiction.