We show that thermodynamic description is admissible only while the state remains within an operational identity region under irreversible dynamics. At finite operational resolution, identification as a system induces a finite distinguishability margin relative to a reference baseline. Under admissible dynamics that contract distinguishability, this margin is monotonically depleted, yielding a bound on the interval over which thermodynamic quantities can be consistently assigned. The result is not a new inequality, but a structural interpretation of a known contraction property with direct consequences for the admissibility of thermodynamic description. Monotonic depletion of divergence is typically treated as a constraint on trajectories; here it is shown to define a prerequisite for thermodynamic description itself, with loss of admissibility corresponding in the radial case to a first-exit event from the identity region. The second law appears as the thermodynamic representation of this constraint when expressed in entropy coordinates. Four consequences follow: thermodynamic description has a finite descriptive horizon; persistence beyond the passive first-exit time requires support from auxiliary degrees of freedom; loss of descriptive validity is a first-exit event from an operational boundary; and in non-radial systems scalar persistence descriptions based on divergence alone are incomplete, as trajectories with identical cumulative depletion can lose admissibility at different times depending on boundary geometry. The framework yields a quantitative diagnostic for model completeness and applies uniformly to classical and quantum systems within the class of admissible (contractive) dynamics.
Dimitri Cerny (Mon,) studied this question.