Admissibility, Irreversibility, and Finite Resolution in Navier–Stokes Dynamics

Boundary and Scope Notice (CRL-0): This document is observer-only and non-authoritative. Any method-like descriptions, contrasts, figures, or illustrations are interpretive and non-normative; they are not offered as deployment guidance, certification criteria, or operational decision rules. No recommended calibration, thresholds, protocols, or implementation guidance are provided. Any evaluable instantiation belongs to downstream evaluation artifacts. Structural claims and results are unchanged. This paper provides the thermodynamic closure of the Constraint Program by showing that irreversibility, entropy production, and constraint cost are unavoidable consequences of admissibility enforcement under finite resolution. Rather than introducing new primitives, this work shows that once any system enforces structural admissibility—whether physical, computational, or organizational—thermodynamic cost emerges necessarily, independent of domain, implementation, or intent. Irreversibility is not assumed, optimized, or statistically inferred; it follows directly from finite resolution and the suppression of inadmissible trajectories. The analysis reframes entropy not as a probabilistic artifact or informational proxy, but as a structural consequence of constrained evolution. Constraint enforcement eliminates neutral paths, induces directional bias in state space, and renders certain transitions non-invertible. These effects persist even in idealized systems with perfect local rationality, zero noise, and correct internal models. This paper does not propose a new thermodynamic theory. Instead, it demonstrates that any admissibility-preserving system necessarily pays a constraint cost, and that classical thermodynamic behavior arises as a downstream manifestation of this requirement. This work serves as the closure of an admissibility sequence, explaining why irreversibility, entropy, and energy dissipation must appear once admissibility is enforced, rather than treating them as axioms or empirical add-ons.