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

Official website: distinctiontheory.orgPublic portal for the start guide, papers, claim status, failure registry, prior-art boundary, and citation resources. Canonical GitHub repository:https://github.com/yiningwu-research/Distinction-Theory 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. This 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, that all irreversibility is Landauer erasure, 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. At least one channel must change: residual turnover is reduced, the task tolerance is relaxed, entropy is produced or exported, resources expand, passive degradation is accepted, or the boundary-maintenance regime fails. The paper introduces task-relevant record load, record-reuse pressure, boundary-relative residual irreversibility, finite-window residual record-turnover rate, an audited O3 entropy ledger, record-equivalent exit relief, a finite-register operational equilibrium analogy, a record-turnover power floor, pruning dissipation return on investment, and invariant compression with over-compression penalties. The accompanying replication package includes deterministic synthetic simulations, figures, CSV outputs, LaTeX source, and Python code. The 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. Scope. FDS-O3 does not replace statistical mechanics, fluctuation theorems, or stochastic thermodynamics. It supplies a finite-record operational channel connecting FDS-P1/P2/P5 to macroscopic irreversibility while preserving the distinction between thermodynamic entropy and record-turnover entropy.