Persistence Beyond Passive Margin Exhaustion: Geometric Non-Closure and Distinguishability Allocation

“Persistence Beyond Passive Margin Exhaustion: Geometric Non-Closure and Distinguishability Allocation” The paper investigates when coarse-grained subsystem descriptions necessarily fail to remain dynamically closed under irreversible dynamics. Existing stochastic thermodynamics typically assumes that the reduced subsystem description remains valid and asks how entropy production is redistributed within it. This work instead asks the logically prior question: when must the passive reduced description itself fail to close? For radial operational identity regions defined by distinguishability level sets, the passive reduced dynamics admits a complete scalar persistence descriptor up to a finite passive margin exhaustion time τ*. The paper proves that persistence beyond τ* forces the observed joint trajectory to deviate from its passive reference: the passive reduced description fails to close, and complement degrees of freedom necessarily participate in the deviation. The resulting support structure is organized by the exact allocation identity o (t) = i (t) + σₑxcess (t), where i (t) is the input support current, o (t) is the complement allocation flux, and σₑxcess (t) is the excess dissipation. The sign of σₑxcess distinguishes driven support from stabilization support. Under Gibbs reference conditions, the driven-support regime obeys a free-energy maintenance lower bound proportional to kB Tₑnv λ Dₑxit (T − τ*). The manuscript develops: - the geometric non-closure theorem, - the distinguishability-allocation structure, - the maintenance-work bound, - the lifecycle extension of Landauer erasure, - and the allocation-resolved thermodynamic uncertainty relation. Numerical and empirical validation includes: - a four-state Markov model verifying the allocation identity to numerical precision, - DRAM retention analyses using SAFARI retention distributions, - and superconducting-qubit crossover calculations for logical memory on the Willow processor. The DRAM analysis shows that more than 99. 7% of tested cells possess passive persistence horizons shorter than standard operational refresh intervals, placing practical DRAM in the maintenance-dominated regime. The resulting maintenance burden exhibits measurable weak-tail heterogeneity rather than extreme Pareto concentration: the weakest 10% of cells account for approximately 15% of the predicted thermodynamic maintenance burden, while the weakest 20% account for approximately 30%. Superconducting logical-memory calculations exhibit the predicted crossover from the Landauer-dominated regime to the maintenance-dominated regime as logical-memory persistence exceeds the passive physical-qubit lifetime. Together these results establish a two-stage diagnostic criterion: persistence beyond τ* certifies passive reduced non-closure, and the sign of σₑxcess identifies the support regime once closure fails.