Irreversibility by Singular Limits: An Ontological Account of Turbulent Dissipation (Euler, Onsager, and the Defect Measure)

We argue that turbulent irreversibility is best explained as an asymptotic feature of a singular inviscid limit—a reclassification of admissible entities and balances at ν→0—rather than as a mere residual effect of molecular viscosity. Tracing a conceptual line from Euler and Kármán–Howarth to Onsager, Duchon–Robert, Kato/Prandtl, and modern convex integration results, we show that the limit theory reclassifies the admissible entities: from smooth Euler fields (energy conserving) to rough weak solutions equipped with a positive defect measure in the energy balance. The constant inter-scale process (energy flux) observed at high-Reynolds number therefore persists at ν=0 as a structural feature of the limit ontology. We articulate three selection principles—the local energy inequality, the exact third-order law, and scale-locality—as ontological constraints that reconcile mathematical non-uniqueness with physical uniqueness. A brief conceptual history clarifies how the arrow of time in turbulence emerged through successive shifts of entities and invariants, and a comparison with other singular limit explanations (Boltzmannian irreversibility, shocks, renormalization) situates the account within general foundations of physics. Methodologically, we recast LES/closures as asymptotic mediators validated by flux plateaus and viscosity-free diagnostics, not microscopic subgrid fidelity.