The Structural Origin of Irreversibility Coherence, Reconstructibility, and the Arrow of Time

This work introduces structural coherence as a criterion that distinguishes mathematically admissible solutions from physically realizable configurations. Many physical theories allow vast families of formal solutions, yet only a small subset can persist under irreversible dynamics. Structural coherence captures this distinction by quantifying the persistence of multiscale informational correlations through mutual information. Using this framework, we show that irreversibility arises not from fundamental asymmetries in the equations, but from the structural loss of coherence that makes backward reconstruction ill‑posed. Even when the microscopic dynamics are time‑reversible, the effective dynamics destroy the correlations required to recover past states, producing an emergent arrow of time. Three‑dimensional Navier–Stokes turbulence serves as a minimal physical laboratory: multiscale vorticity features exhibit monotonic decay of temporal coherence and a strong asymmetry between forward prediction and backward reconstruction. These results illustrate how coherence acts as a structural selection mechanism, filtering out configurations that cannot be dynamically sustained. Overall, the framework provides a physically grounded criterion for viability, clarifies the origin of irreversibility, and offers a unified perspective on why only a small fraction of mathematically possible configurations ever manifest in the physical world.