A Spectral Energy Framework for Non‑Markovian Model Reduction Error via Mori–Zwanzig Commutation Defects

We present a rigorous spectral framework for quantifying non‑Markovian model‑reduction error in multiscale Markov generators. Using the Mori–Zwanzig commutation defect , we show that the short‑time growth of the memory kernel is controlled by the spectral energy of the defect under explicit spectral‑gap and analytic‑semigroup assumptions. We also introduce a spectral entropy functional describing the dispersion of the defect across fiber modes. The result provides a coordinate‑independent characterization of memory generation in coarse‑grained dynamics.