Relativistic Limits of Decoding: Critical Divergence of Kullback-Leibler Information and Free Energy

TL;DR

This paper develops a statistical mechanical framework using Kullback-Leibler divergence to analyze the limits of decoding information from moving sources at relativistic speeds, revealing phase-transition-like behavior.

Contribution

It introduces a novel relativistic information theory model linking KLD, Fisher information, and free energy to decoding stability near light speed.

Findings

KLD diverges as velocity approaches the speed of light

Decoding sensitivity becomes unstable near relativistic limits

A critical velocity exists beyond which decoding fails thermodynamically

Abstract

We present a statistical mechanical framework based on the Kullback-Leibler divergence (KLD) to analyze the relativistic limits of decoding time-encoded information from a moving source. By modeling the symbol durations as entropy-maximizing sequences and treating the decoding process as context-sensitive inference, we identify KLD between the sender and receiver distributions as a key indicator of contextual mismatch. We show that, under Lorentz transformations, this divergence grows with the sender's velocity and exhibits critical divergence as the velocity approaches the speed of light. Furthermore, we derive an analytic expression for the Fisher information and demonstrate that decoding sensitivity diverges similarly, indicating instability near the relativistic limit. By introducing an information-theoretic free energy based on the decoding cost, we determine a critical velocity beyond which decoding becomes thermodynamically impossible. These results reveal a phase-transition-like behavior in relativistic information transfer and provide a unified interpretation of KLD, Fisher information, and free energy as measures of decodability. The formalism developed here offers new insights into high-speed communication, relativistic signal processing, and information geometry in non-inertial frames.