Structural Differentiation Time (SDT): Emergent Time from Irreversible Information Accumulation

This work introduces Structural Differentiation Time (SDT), a minimal, decisive, and falsifiable framework in which time is not assumed as a fundamental parameter, but emerges from irreversible structural information accumulation. In SDT, structural differentiation produces distinguishable differences, observation stabilizes these differences as information, and accumulated information manifests as emergent time. The framework is defined by three core relations: (1) Structural-to-informational mapping: Iₛtruct ∝ −log (1 − ηD) (2) Emergent time from accumulated information: τ = 1 − exp (−k Iₛtruct) (3) Temporal existence condition: dIₛtruct/dt > 0 A key boundary condition is identified: lim₈䂺ₓₑₔ₂ₓ → ₀ τ = 0, indicating that time does not exist in the absence of structural information accumulation. Thus, time is reinterpreted as a conditional and emergent quantity, not a predefined background coordinate. This framework provides a direct and testable connection between structural evolution, information growth, and temporal order, offering a new pathway toward observational and experimental validation. SDT predicts that a physical system exhibits time if and only if it exhibits sustained irreversible structural information accumulation. Time is not assumed — it is generated.