Bruises: The Physics of Imperfect Erasure [Subtitle: A Diagnostic Framework Across Landauer Bounds, Decoherence, and Quantum Error]

Why do some physical processes erase cleanly while others leave persistent traces that shape future evolution? This preprint argues that “irreversibility” means different things in different contexts—and that conflating these meanings generates systematic confusion across quantum error correction, decoherence theory, and thermodynamics of information. We establish a diagnostic framework: physical processes that resist perfect reversal can be characterized along four partially independent axes: (1) logical irreversibility (many-to-one maps), (2) thermodynamic cost (dissipation under Landauer-type constraints), (3) dynamical irreversibility (non-reversibility under realistic control sets), and (4) record usefulness (accessible correlations meeting reliability criteria). These axes are necessary conditions for persistent state-dependent significance, but their relationships are implementation-dependent, not universal implications. The contribution is diagnostic organization with experimental grounding rather than new physical mechanisms. We introduce the “bruise”—pedagogical shorthand for the minimal failure of perfect erasure—as cross-domain vocabulary connecting Landauer erasure experiments (Berut et al.), quantum Darwinism measurements (Ciampini et al., Riedel & Zurek), and fault-tolerant syndrome extraction (Google Quantum AI). The framework makes explicit what existing terminology sometimes obscures: when thermodynamic cost implies record formation (Landauer regime), when it does not (Szilard regime), and how control-set switching generates pseudo-disagreements. The analysis provides experimental protocols and clarifies relationships across multiple domains: ∙ Landauer bounds & Maxwell demons (complementarity of dissipation vs. record retention) ∙ Decoherence & quantum Darwinism (pure dephasing vs. dissipative channels as distinct record-formation mechanisms) ∙ Quantum error correction (syndromes as “good bruises,” logical errors as “bad bruises”) ∙ Commitment depth (qualitative design diagnostic, not universal metric) ∙ Control-relative irreversibility (formalizing Zurek’s insight that reversibility depends on available operations) Rather than proposing new physics, the paper demonstrates that canonical pedagogical confusions (measurement reversibility debates, decoherence vs. record formation, logical vs. thermodynamic irreversibility) arise from implicit axis conflation. Making diagnostic structure explicit prevents miscommunication. Each axis includes: ∙ Mathematical formalization (state spaces, semigroup structure, distance metrics) ∙ Experimental measurement protocols with quantum caveats ∙ Mapping to recent experimental results with corrected values ∙ Quantitative thresholds for operational criteria Relevant to: quantum error correction practitioners, decoherence theorists, thermodynamics of information researchers, foundations of physics, quantum computing experimentalists, and anyone teaching irreversibility across physics subfields. Pedagogical tool: Includes “Bruise-Formation Hygiene Checklist” for avoiding common conceptual errors in cross-domain discussions.