Infrared Scaling Criterion for the Asymptotic Validity of Local Master Equations

Local (Markovian) master equations provide a standard framework for describing the dynamics of open quantum systems, yet their asymptotic range of validity is typically assessed through weak-coupling or short-memory assumptions rather than explicit infrared scaling properties. Here we formulate a model-independent infrared scaling criterion that delineates the regime in which local master equations organize asymptotic dynamics. The analysis is based on the infrared structure of the retarded kernel, where the analytic local contribution is characterized by an exponent n_IR, while the spectrally induced self-energy scales as (−iω)^γ. This formulation isolates the infrared scaling competition independently of microscopic details of the bath realization. A direct comparison of these exponents yields a simple diagnostic condition: local descriptions control the infrared scaling only when the analytic contribution remains dominant, whereas for γ < n_IR the non-analytic spectral term becomes infrared dominant and determines the long-time behavior. The criterion is illustrated with representative examples, including regimes where local equations remain asymptotically valid and the sub-Ohmic case where infrared spectral dominance leads to non-exponential relaxation. These results provide a compact infrared scaling diagnostic for the asymptotic validity of local master equations without introducing additional dynamical assumptions.