Phase Transition Thresholds as Admissibility Boundaries

Phase transitions mark abrupt changes in macroscopic behaviour when a physical system crosses a critical threshold in its governing parameters. Traditional thermodynamic interpretations describe these transitions through order parameters, critical exponents, and symmetry changes. This paper interprets phase transitions through the admissibility framework of the Paton System. Under this interpretation, phase transitions occur when the set of structurally admissible configurations of a system changes discontinuously as governing constraints shift. The critical point therefore represents a boundary between admissible configuration regimes. Phase transitions can therefore be understood as structural reorganisations of admissible configuration manifolds under changing physical constraints. This interpretation unifies thermodynamic phase transitions with other constraint-defined transitions observed in physical systems, including turbulence onset, gravitational collapse, and cosmological structure formation. The paper is presented as a Tier-7 physical systems domain instantiation within the Paton System framework.