Dynamic Harmony Structural Stress-Test Series. This paper evaluates the role of instability and irreversibility in nonequilibrium thermodynamics as developed in the work of Ilya Prigogine. The analysis examines whether irreversible processes and far-from-equilibrium instabilities provide a sufficient structural account of the emergence of ordered physical systems. Using the Phase Non-Substitutability Test introduced in Paper 0 and the architectural boundary criterion developed in Paper 0B, the paper analyzes whether dissipative instabilities represent genuine architectural redefinition or whether they remain configurational rearrangements within an existing thermodynamic state space. The analysis clarifies the structural limits of purely physical emergence and examines the conditions under which thermodynamic processes can produce persistent organized structures. This paper forms part of the Dynamic Harmony Structural Stress-Test Series, a research program that evaluates major theories of emergence across physics, biology, and complex systems through adversarial structural analysis