Bounded-Memory Reversible Computation and Housekeeping Dissipation: Garbage Entropy Rate, Active Forgetting, and Finite Reuse

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-P2 develops the second paper in the Physical Bridge Ladder of Active Finite Distinction Systems. Building on FDS-P1, it studies bounded-memory reversible computation as a finite-record accounting problem. Reversible computation can avoid immediate Landauer-style erasure by retaining enough side information to make an enlarged update invertible. Under bounded memory, however, this strategy accumulates garbage records that must be carried, refreshed, synchronized, uncomputed, externalized, compressed, cleaned, or abandoned. The paper defines garbage entropy rate, accumulated residual irreversibility, nonlinear memory-fill pressure, uncomputation versus irreversible cleanup, externalization as an accounting-boundary shift with latency, active forgetting through lossy compression, and a resource-dependent housekeeping optimization problem. The central theorem states that a bounded-memory system executing sustained reversible updates with positive garbage entropy rate cannot continue indefinitely without uncomputation, cleanup, compression, externalization, task relaxation, memory expansion, or failure. This paper does not refute reversible computation, does not claim that every computational step dissipates kBT ln 2, does not invalidate quantum reversible computation, and does not derive Landauer's principle. Its narrower contribution is a finite-record accounting model: reversibility changes the time profile and location of dissipation, but bounded memory makes retained inverse information itself a physical burden. The accompanying replication package includes deterministic synthetic simulations, figures, CSV outputs, LaTeX source, and Python code. The simulations illustrate correlated garbage entropy rate, nonlinear memory-fill pressure, cleanup heat spikes, accumulated residual irreversibility, uncomputation versus cleanup, cleanup scheduling tradeoffs, externalization latency, active forgetting through lossy compression, bounded-memory regimes, and high-rate syndrome-style record turnover as a conservative domain projection. Scope and boundary. The syndrome-style record section is not a quantum-computing no-go theorem and not a claim that all quantum error-correction architectures are thermodynamically impossible. It only identifies syndrome production, reset, decoding, latency, and finite-memory turnover as instances of the bounded-record accounting problem.