Phase Transitions: An Interpretation as Containment Expansion

This research paper presents a novel theoretical framework for understanding phase transitions not merely as changes in physical parameters, but as containment expansions, formally expressed as Aₖ → A_ (k+1), and increases in structural depth Redefining the transition from a phase Aₖ to A₊+₁, the author demonstrates that new organizational layers emerge as the system's configurational diversity exceeds a critical threshold (ₖ > c). Through an information-theoretic perspective, the study establishes that every phase transition results in the embedding of the previous state within a new structural layer (Aₖ A₊+₁). Key concepts explored: Structural Depth Theory in physical systems. Configuration Space expansion and reorganization. Containment Relations in complex thermodynamics. Energy confinement and structural evolution. This work contributes to a unified theory of structural evolution, bridging concepts from theoretical physics, systems theory, and the Structural Depth Law of Time.