A Thermodynamic Constraint on Persistence

It is shown that persistence is necessarily bounded when identity is defined at finite operational resolution and the dynamics contract distinguishability on the operational state space. Any such identity possesses a finite distinguishability margin that is monotonically depleted under irreversible evolution, yielding a persistence-time bound determined by the margin and the mean depletion rate. The bound is operationally predictive whenever the depletion rate can be characterized independently — as in thermodynamically well-characterized systems including isothermal relaxation, discharge processes, and phase transitions — and functions as a constraint on admissible irreversible histories otherwise. This result follows from two structural assumptions: finite-resolution identity relative to a reference baseline and irreversible dynamics that contract distinguishability. The bound can be expressed in information-geometric terms and is accordingly applicable across physical substrates; in Markovian settings thermodynamic entropy production provides a direct realization through relative-entropy decay identities. The persistence constraint further acts as an admissibility criterion for open-system boundaries. Boundaries are admissible only if they enclose sufficient organizational coherence to maintain distinguishability under the prevailing dynamics; boundaries that partition the structure responsible for maintaining the reference baseline yield incoherent persistence descriptions. This admissibility criterion appears to sort physical interactions by whether they admit closed operational descriptions — a structural distinction with implications beyond the modeling contexts considered here. The framework therefore provides an explicit criterion for when the persistence assumption is physically admissible, a modeling assumption that is widely used but rarely stated explicitly in descriptions of open systems across physics, biology, and information-theoretic settings.