Clockability: An Operational Criterion for Internal Time in Physical Systems

The concept of time is often implicitly associated with dynamical evolution, periodicity, or entropy increase. In this work, we adopt a strictly operational and non-ontological perspective and ask a narrower question: under which conditions can a physical system define a time internally for itself?We introduce the notion of clockability as an operational criterion for the existence of an internal temporal structure and use it as a diagnostic tool rather than as a theoretical proposal. By analyzing systems where temporal order appears to exist—such as oscillatory systems, time crystals, and entangled quantum states—we identify informative exceptions in which temporal order does not correspond to internal time. We show that periodicity, temporal symmetry breaking, correlation, and entropy increase are not sufficient for clockability. Instead, clockability requires irreversible selection with non-cancelable accumulation of state information. This leads to a classification of temporal regimes and to an operational no-go result: many physically relevant systems exhibit temporal order without possessing an internal time. The analysis introduces no new physical laws and remains fully compatible with standard quantum and statistical mechanics.