The Entropic Grain Boundary Stabilization Theorem: A Unifying Thermodynamic Criterion for Polycrystalline Stability Under Cyclic Thermal Loading

The thermal stability of polycrystalline microstructures under cyclic loading remains a fundamental unsolved problem in physical metallurgy. Classical theories predict inevitable grain coarsening, yet high-entropy alloys exhibit anomalous stability. Here we present the Entropic Grain Boundary Stabilization The orem (EGBST),arigorous thermodynamic framework that resolves this paradox. We prove the existence of a critical configurational entropy density threshold 𝑆∗ 𝑐(𝑇,𝜎) that determines whether grain boundary migration is thermodynamically irreversible. The master equation 𝑆∗ 𝑐 = 𝑘B[𝑍lnΩGB −𝛾GB𝐴GB/(𝑇𝑘B)] unifies three physi cal pillars: configurational entropy, interfacial energy, and cyclic thermal loading. Two corollaries emerge: the Grain Locking Con dition (𝑆config ≥ 𝑆∗ 𝑐 produces entropy-stabilized polycrystals) and the Thermal Hysteresis Window (Δ𝑇𝐻 ∝ √︁ 𝑆∗ 𝑐/𝛾GB). The theorem is derived from first principles using statistical mechanics and the Clausius inequality, validated against published datasets across five alloy families, and provides a quantitative design protocol for grain boundary engineering. This work establishes entropy as a funda mental stabilization mechanism in polycrystalline materials.