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

Many physical theories admit a vast space of mathematically valid solutions, only a small fraction of which ever manifest as observable, persistent configurations. This work proposes structural coherence as an eliminative criterion that distinguishes mathematically admissible solutions from physically viable ones. Coherence is defined operationally as the persistence of informational correlations across time and scales, quantified through mutual information. We show that, even in systems governed by time-reversible equations, the effective loss of coherence leads to an irreversible degradation of reconstructibility. In this sense, irreversibility does not arise from logical or thermodynamic prohibitions, but from a structural obstruction: the information required to reconstruct past states ceases to exist as a stable, exploitable structure. This framework is illustrated using three-dimensional Navier–Stokes turbulence as a minimal physical laboratory. Multiscale features extracted from vorticity fields exhibit a monotonic decay of temporal coherence and a marked asymmetry between forward prediction and backward reconstruction, despite the formal reversibility of the underlying equations. The results support a view in which the arrow of time emerges as the direction of coherence loss, rather than as a fundamental postulate. More generally, structural coherence provides a physically grounded criterion for assessing the realizability of configurations, with implications for irreversibility, effective dynamics, and the interpretation of physically admissible solutions.