Boundary Maintenance and the Second Law under Finite Memory: Irreversible Record Reuse, Entropy Ledgers, and Operational Time Arrows

This paper(FDS-O3) develops the third paper in the Operational Trident. O1 treated observation as finite stable record formation, O2 treated register time as causally ordered irreversible update, and O3 treats the Second Law as an operational channel instantiated by finite-memory boundary maintenance. The paper does not rederive the Second Law from distinction alone. It does not claim that mathematical coarse-graining is heat, that every update dissipates kBT ln 2, or that topological invariants violate thermodynamics. Its narrower claim is conditional: in a physically realized active finite distinction system, finite memory turns sustained boundary maintenance into record reuse; record reuse creates residual irreversibility unless inverse information remains available in side records; and physical overwrite, cleanup, refresh, repair, synchronization, or externalization must be accounted for in a coupled entropy or resource ledger. The central theorem states that sustained residual record turnover, fixed boundary-maintenance tolerance, and zero coupled-system entropy/resource cost cannot persist indefinitely under finite memory and physical bridge assumptions. Deterministic simulations illustrate memory-fill pressure, residual irreversibility, finite-record entropy ledgers, externalization audits, pruning return on investment, invariant compression, overload hysteresis, and finite-memory regime diagrams. O3 thereby supplies a finite-record operational channel connecting FDS-P1/P2/P5 to macroscopic irreversibility without claiming to replace statistical mechanics or stochastic thermodynamics.