Title: Relativistic Limits of Decoding: Critical Divergence of Kullback-Leibler Information and Free Energy Show Chinese title

Title: 相对论解码极限：Kullback-Leibler信息和自由能的临界发散

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. Show Chinese abstract

Abstract: 我们提出了一种基于Kullback-Leibler散度（KLD）的统计力学框架，用于分析从运动源中解码时间编码信息的相对论极限。 通过将符号持续时间建模为熵最大化序列，并将解码过程视为上下文敏感的推理，我们确定了发送方和接收方分布之间的KLD是上下文不匹配的关键指标。 我们表明，在洛伦兹变换下，这种散度随着发送方的速度增加，并且当速度接近光速时表现出临界发散。 此外，我们推导了Fisher信息的解析表达式，并证明解码灵敏度也会类似地发散，表明在相对论极限附近存在不稳定性。 通过引入基于解码成本的信息理论自由能，我们确定了一个临界速度，超过该速度后解码在热力学上变得不可能。 这些结果揭示了相对论信息传输中的相变行为，并提供了一个统一的解释，将KLD、Fisher信息和自由能作为可解码性的度量。 这里开发的形式主义为高速通信、相对论信号处理以及非惯性框架中的信息几何提供了新的见解。