Heating, Ventilation, and Air-Conditioning (HVAC) systems account for a substantial share of global building energy use, making reliable anomaly detection essential for improving efficiency and reducing emissions. Classical rule-based approaches offer explainability but lack adaptability, while deep learning methods provide predictive power at the cost of transparency, efficiency, and physical plausibility. Recent attempts to use Large Language Models (LLMs) for anomaly detection improve interpretability but largely ignore the physical principles that govern HVAC operations. We present PILLM, a Physics-Informed LLM framework that operates within an evolutionary loop to automatically generate, evaluate, and refine anomaly detection rules. Our approach introduces physics-informed reflection and crossover operators that embed thermodynamic and control-theoretic constraints, enabling rules that are both adaptive and physically grounded. Experiments on the public Building Fault Detection dataset show that PILLM achieves state-of-the-art performance while producing diagnostic rules that are interpretable and actionable, advancing trustworthy and deployable AI for smart building systems.