The Physics of Thought: Reasoning as Thermodynamic Relaxation in Generative Models

Large language models exhibit strong reasoning abilities through chain-of-thought generation, yet the mechanisms underlying these processes remain poorly understood. We propose a thermodynamic framework that models reasoning as energy minimization in learned landscapes, establishing formal links between statistical physics and emergent reasoning. Token sequences correspond to microstates, reasoning trajectories follow energy relaxation dynamics, and metacognitive uncertainty arises from entropy gradients. We implement energy-enhanced transformers that explicitly parameterize local energy landscapes, enabling real-time confidence estimation and early termination. Theoretically, we show that chain-of-thought generation minimizes a free-energy functional F (x) = E(x) − T S(x), balancing accuracy and exploration. Empirically, free-energy reduction robustly predicts reasoning success (R2 = 0.89, p < 0.001), with harder tasks exhibiting rougher landscapes. Our approach improves accuracy on challenging reasoning benchmarks by 4 percentage points (pp) over standard models (72% vs. 68%) while reducing inference cost by 22% through early termination, providing both diagnostic insights and practical improvements for AI reasoning systems.