The Informational Luminosity Law (ILL): Empirical Foundations of the Diffusion of Information Hypothesis

This paper introduces the Hunt–Lyra Informational Luminosity Law (ILL) — the first quantitative expression linking stellar energy output to informational flow, derived directly from Landauer’s thermodynamic limit.   The ILL proposes that a star’s rate of information emission is directly proportional to its luminosity and inversely proportional to its surface temperature, establishing a measurable connection between radiative power and the diffusion of information.   Applied to benchmark stars including the Sun, Sirius A and B, Vega, Procyon A, and Betelgeuse, the law reveals a consistent, scalable relationship between thermodynamic behaviour and informational dissipation. Cooler but more luminous stars radiate vastly greater informational flux than compact, hotter objects — unifying stellar physics and information theory within a single framework.   Building upon the Diffusion of Information Hypothesis (DoIH) and the emerging field of Informational Cosmology, this work marks the transition of the diffusion paradigm from conceptual to empirical science. The paper provides clear, testable predictions for astrophysical validation using observational data from Gaia, JWST, and future missions such as Athena.   The ILL thus positions information as a physical quantity that governs energetic processes across the cosmos, establishing Informational Cosmology as a measurable, data-driven discipline.