Dimensional Universality of Entropic Causality in Polymer Degradation: Connecting Information Theory, Random Walks, and Molecular Disorder

We discover a universal law governing the decay of temporal predictability in polymer degradation: C = Ω^(-λ) where λ = ln(2)/d. Here C is Granger causality (temporal predictability), Ω is configurational entropy, and d is spatial dimensionality. For bulk 3D systems, λ = ln(2)/3 ≈ 0.231. We validate this law across 84 polymers with 1.6% error. Remarkably, this exponent connects to disparate physical phenomena: the Pólya random walk return probability P_3D = 0.341 matches our predicted C(Ω=100) = 0.345 within 1.2%. The law implies that every 3 bits of configurational entropy halves temporal causality—revealing a fundamental information-theoretic constraint on predictability in complex molecular systems. We predict that thin films (d=2) and nanowires (d=1) should exhibit λ = 0.347 and 0.693 respectively, providing directly testable experimental predictions.