[
  {
    "id": "ARR-2025-76C3S3SSMP8HJ8NF-v1",
    "type": "article",
    "title": "The Conditional Maintenance Work Theorem: Operational Power Lower Bounds from Energy Pinching and a Split-Inclusion Blueprint for Type III AQFT",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2025,
          12,
          16
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2025-76C3S3SSMP8HJ8NF",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2025-76C3S3SSMP8HJ8NF/versions/v1/",
    "note": "Archived manuscript; ARR-2025-76C3S3SSMP8HJ8NF v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "We derive operational lower bounds on the minimal thermodynamic power required to maintain quantum coherence against uncontrolled open-system dynamics. Work is defined as the consumption of non-equilibrium free energy stored in an explicit battery at bath temperature T, namely W := F_W(sigma_W) - F_W(sigma'_W) with F_W(sigma) = k_B T S(sigma||gamma_W), and allowed controls are battery-assisted thermal operations implemented by energy-conserving global unitaries. Coherence is quantified as a relative entropy to a conditional expectation, C_E(rho) := S(rho||E[rho]). Our main proved results are: (i) an unconditional maintenance bound P_min(rho) >= k_B T sigma(rho), where sigma(rho) >= 0 is the entropy production rate of the target under the uncontrolled semigroup (Spohn), which splits via the pinching Pythagorean identity as sigma = F_diag + C_loss; (ii) the coherence-power bound P_min >= k_B T C_loss(rho) under a diagonal-contraction hypothesis satisfied by Davies generators; and (iii) extra-power bounds for coherence stabilization relative to thermodynamically efficient population-maintenance baselines — version 1's \"assumption-free\" paired-infimum formulation is shown to be vacuous (the unlinked-pairs infimum is minus infinity), and the corrected statement is genuinely assumption-free precisely when the pinched target is stationary (e.g. pure dephasing), where the baseline is free. We further provide a conditional extension to general conditional expectations and a Type III split blueprint, with external geometric inputs encoded as explicit two-sided interface assumptions. All finite-dimensional claims are verified by an exact numerical suite distributed with the paper. These results provide an operational resource criterion for quantum-to-classical behavior, not a collapse theory.Version 2 corrects a sign error in the work definition and in the final step of v1's Appendix A, replaces v1's vacuous extra-power definition, and strengthens the main bound to an unconditional entropy-production form."
  }
]