Thermodynamic Signatures of Reasoning: Free-Energy and Spectral-Form-Factor Diagnostics for Hallucination Detection in Large Language Models

The article presents a novel method for hallucination detection in large language models (LLMs) using Free-Energy Signatures (Fes), which analyzes the spectrum of attention-derived graph Laplacians. Fes extracts thermodynamic potentials and offers improved performance over existing methods, achieving a +6.5 AUROC point increase over LapEig and +2.4 points over GoR-4 across six benchmarks with no updates to the underlying models. This approach enhances the interpretability of reasoning quality in LLMs and provides a robust, training-free detection mechanism, which is critical for deploying reliable AI systems.