Clockability as an Operational Criterion for the Validity of Time-Local Descriptions in Open Quantum Systems

This technical note introduces clockability as an operational criterion for assessing the validity of time-local descriptions in open quantum systems. While non-Markovian dynamics are commonly characterized through information backflow or violations of CP-divisibility, the structural conditions under which a temporal description remains operationally meaningful are rarely made explicit. This work reframes non-Markovianity not as a dynamical anomaly, but as a signal of local clockability breakdown: the failure of the environment to function as a stable register of persistent and locally accessible traces. Within this framework, CP-divisibility emerges as a sufficient condition for local clockability, whereas its violation marks the loss of applicability of time-local master equations rather than a failure of quantum dynamics itself. The note clarifies the relationship between divisibility-based and information-theoretic measures of non-Markovianity and motivates a hierarchical domain-of-validity analysis for temporal descriptions. No new physical mechanisms or mathematical formalisms are introduced. Instead, the work provides a diagnostic, information-theoretic perspective on when time-local representations (e.g., GKSL forms) are structurally justified, and when dynamical descriptions should be interpreted as non-local, history-dependent responses. This contribution is intended as a conceptual and methodological clarification relevant to quantum information theory, open quantum systems, and the operational foundations of time.