Finite Descriptive Horizon for Thermodynamic Systems Under Contractive Dynamics

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.