Intrinsic Criticality in Transport-Type Evolution Equations

This paper examines a broad class of transport-type evolution equations whose generators admit a decomposition into symmetric and antisymmetric components, possibly augmented by nonlocal projection constraints. It is shown that norm growth is entirely governed by the quadratic form associated with the symmetric component, while the realization of sustained growth requires persistent alignment with expanding directions. The analysis establishes that such alignment is generically disrupted by antisymmetric transport through non-commutativity and is further destabilized by projection-induced modifications of admissible directions. Consequently, growth remains dynamically accessible but cannot be stabilized over time. This structural mechanism gives rise to an intrinsically critical regime that does not depend on fine-tuning, special symmetries, or equation-specific cancellations. The results provide a unified structural perspective on why many transport-dominated problems resist definitive classification into uniformly stable or unstable regimes and exhibit persistent transient and near-critical behavior.