Persistence Beyond Passive Margin Exhaustion: Geometric Necessity and Distinguishability Allocation

Persistence Beyond Passive Margin Exhaustion: Geometry, Thermodynamics, and Distinguishability Allocation. The work studies persistence under irreversible dynamics using a geometric and thermodynamic framework based on contractive distinguishability margins. The central result is that persistence beyond the passive margin exhaustion time τ* implies dynamical non-closure of the passive reduced description: the observed subsystem trajectory cannot be generated by passive reduced dynamics alone. This follows from contractivity and the chain rule on the joint distinguishability margin, without thermodynamic assumptions. The framework introduces three trajectory-level quantities — the input support current, complement allocation flux, and excess dissipation — linked by the exact allocation identity o (t) = i (t) + σₑxcess (t), which functions as a diagnostic completion test for reduced descriptions. The sign of σₑxcess distinguishes two physically distinct support regimes: a driven support regime, where external throughput drives persistence against passive contraction, and a stabilization support regime, where feedback suppresses joint depletion relative to the passive reference trajectory. Under irreversible driven support and exponential passive contraction, the work cost of persistence is bounded below by kB T λ Dₑxit (T − τ*), providing the continuous-maintenance complement to Landauer’s erasure principle. The repository includes: - Four-state Markov-model simulations verifying the allocation identity numerically to machine precision- DRAM persistence analyses based on SAFARI retention datasets- Processed retention distributions and maintenance-floor calculations- Figure-generation scripts and publication-ready figures- Reproducibility tables used in the manuscript Empirical SAFARI DRAM analyses show that more than 99. 7% of tested cells exhibit passive persistence horizons shorter than standard operational refresh intervals, placing practical DRAM in the maintenance-dominated regime. Applying the driven-support bound to the full retention distribution reveals a strongly concentrated maintenance burden: the shortest 10% of cells account for 54. 3% of the total predicted thermodynamic maintenance cost.