Capacity Deficit and Entropy Production in Active Finite Systems: A Generalized Dissipation Ledger for Boundary Maintenance

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-P5 develops a physical bridge between task-relative capacity deficit and entropy-production pressure in Active Finite Distinction Systems. It builds on the FDS formal core, FDS-P1, FDS-P2, FDS-N1, and FDS-T3. A capacity deficit Δε(τ) > 0 is not heat, entropy production, or thermodynamic irreversibility by itself. It is an information-theoretic shortfall between task-relevant rate-distortion demand and effective capacity. The central claim of this paper is narrower: when a physically realized active finite system continues boundary maintenance under sustained positive deficit, the required correction, refresh, repair, synchronization, externalization, pruning, or recovery must be accounted for somewhere in a coupled entropy or resource ledger. The paper introduces a generalized entropy-production audit ledger for active finite systems, including an anti-double-counting convention, reservoir-indexed entropy-production notation, a distinction between physical recovery entropy and functional boundary loss, and a correction-flow lower bound tied to rate-distortion deficit. It also defines positive-density deficit windows, capacity-equivalent exit relief, pruning dissipation return on investment, invariant compression relief, and externalization as entropy relocation rather than entropy deletion. The main theorem states that sustained positive capacity deficit, fixed boundary-maintenance tolerance, and zero coupled-system entropy or resource cost cannot persist indefinitely under the P5 physical bridge assumptions. At least one channel must change: the deficit is reduced, the task is relaxed, entropy is produced or exported, resources expand, passive degradation is accepted, or the boundary-maintenance regime fails. The accompanying replication package includes deterministic synthetic simulations, figures, CSV outputs, LaTeX source, and Python code. The simulations illustrate capacity-deficit crossing, unique-channel ledger decomposition, pruning dissipation ROI, coupled-system externalization, invariant compression, maintenance-failure regimes, and entropy-production hysteresis after deficit crossing. Scope. This paper does not claim that every distinction dissipates heat, that every bit of uncertainty costs kBT ln 2, that capacity deficit is thermodynamic entropy, that all entropy production is Landauer erasure, or that the Second Law is newly derived. Its contribution is a finite-system dissipation ledger for boundary maintenance under positive capacity deficit.