Kullback-Leibler Divergence as a Measure of Irreversible Information Loss Near Black Hole Horizons

Abstract

We present a unified theoretical framework that integrates information theory, thermodynamics, and general relativity to analyze the fundamental limit of decoding time-encoded signals in curved spacetime. In particular, we introduce the Kullback-Leibler divergence (KLD) as a quantitative measure of the mismatch between the transmitted and received symbol distributions induced by gravitational time dilation. Using a minimal communication model, we derive the critical radius at which information decoding becomes thermodynamically impossible due to the divergence of the KLD. We show that this radius approaches the Schwarzschild horizon in the limit where the information entropy cost becomes negligible relative to the transmission energy. This result provides a novel information-theoretic interpretation of the event horizon as a boundary of irreversible information loss governed by universal thermodynamic principles. Our framework offers new insights into the entropic and energetic constraints on communication in strong gravitational fields and may extend to general relativistic and quantum information settings.