Geometric and Thermodynamic Constraints on Persistence Beyond Passive Relaxation

Coarse-grained descriptions of open systems implicitly assume that the reduced dynamics accounts for all persistence-relevant structure. This paper shows that assumption fails precisely and measurably: if a subsystem remains distinguishable beyond its passive first-exit time, the passive reduced description is necessarily dynamically incomplete. This geometric non-closure result follows from contractivity alone, independent of thermodynamic assumptions. When the required auxiliary support is implemented irreversibly, strictly positive global entropy production follows from established results in stochastic thermodynamics. Under exponential passive contraction and thermal support, a free-energy maintenance bound is derived that is determined by three independently measurable quantities: the passive contraction rate, the operational resolution threshold, and the observed persistence duration beyond passive exhaustion. The construction identifies two distinct thermodynamic regimes separated by a dimensionless crossover parameter M=λDexitΔTM=λDexitΔT. When M≪1M≪1, boundary-crossing events dominate and Landauer's erasure principle applies. When M≳1M≳1, continuous maintenance dominates and the free-energy maintenance bound applies. This places static CMOS logic in the Landauer-dominated regime and DRAM and biological systems in the maintenance-dominated regime. A four-state Markov model verifies the free-energy maintenance bound numerically. Empirical retention data from SAFARI DRAM datasets confirm that real actively maintained information systems operate in the maintenance-dominated regime, with over 99.7% of tested cells exhibiting passive persistence horizons shorter than standard operational refresh intervals. This work is part of a research program on thermodynamic persistence constraints, developed in companion papers on geometric first-exit structure, finite descriptive horizons, cascade admissibility, and empirical consistency.