A Thermodynamic Threshold for Zero-Day DDoS Detection via Spectral Graph Theory

This paper presents a paradigm shift in cybersecurity: the Spectral Entropy Criterion π{crit}). We demonstrate that centralized DDoS attacks are not merely volumetric anomalies but topological singularities that converge mathematically to a spectral ratio of \Pi=0.5 (Star Graph signature). In contrast, healthy network traffic behaves thermodynamically as a rectified stochastic signal, naturally maintained below the fundamental limit of 2/π ≈ 0.637. By monitoring the Algebraic (Fiedler value) relative to the Average Degree, this method exposes the topological phase transition instantly. The proposed algorithm requires zero training, operates on standard CPUs with a memory footprint of less than 1KB, and achieves detection latencies of under 1 millisecond. Experimental benchmarks demonstrate that this thermodynamic approach is approximately 30,000x more energy-efficient than State-of-the-Art Deep Learning models, establishing a deterministic physical law for network health that renders probabilistic "Black Box" heuristics obsolete.