Relativistic limits of decoding: critical divergence of Kullback–Leibler information and free energy

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 symbol durations as entropy maximizing sequences and treating the decoding process as context sensitive inference, we identify the KLD between 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 behavior as the velocity approaches the speed of light. Furthermore, we derive an analytic expression for the Fisher information and demonstrate that decoding sensitivity diverges in the same limit, indicating instability near the relativistic boundary. By introducing an information theoretic notion of free energy based on decoding cost, we determine a critical velocity beyond which decoding becomes thermodynamically impossible. These results reveal a phase transition 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 noninertial frames.