A Thermodynamic Criterion for Structural Persistence in Open Quantum Systems

The author introduces the Thermodynamic Criterion Index ΦL (t) = − (dSᵥN, L/dt) /σL (t), a dimensionless rate ratio at the thermodynamic boundary L of an open quantum system. For autonomous Spohn-compatible Markovian GKSL dynamics, the second law gives ΦL = 1 − σᵢrr, L/σL ≤ 1, with equality at the Landauer reversibility limit. The sign of Φ classifies dynamics: dissolution (Φ σcut } defines an instantaneous scale-selection principle: at each time t, the selected boundary L* (t) is the autonomous thermodynamic scale that minimises irreversible leakage per unit exported entropy. The time-independent notation L* is used only as a shorthand: either when the same maximising boundary persists over the reported transient window, or when a window-averaged diagnostic is explicitly specified. Structural information is identified with Iₛtruct = D (ρ ∥ ρₑq), the relative entropy to the iso-energetic Gibbs state. The framework is validated on three Markovian models. A thermalising Lindblad qubit verifies the three regimes. Independent-bath two-qubit cases provide a regime-dependent benchmark: in the symmetric case no upward selection is observed within the controlled benchmark (analytic at J = 0, numerical for J ≠ 0 under the stated symmetry, parameter and initial-condition assumptions), and in the asymmetric case the composite diagnostic does not exceed the best positive-flux projected local diagnostic in the perturbative-coupling regime, while at larger exchange couplings an operational composite crossing appears in a regime where one local entropy-export rate is negative and the local-bath decomposition is no longer a clean family of autonomous thermodynamic boundaries. A shared Dicke collective bath provides bath-induced upward selection at the composite scale, with peak margin maxₜ ΦᶜollAB (t) − ΦˡocAB (t) = 2. 3708 at t = 0. 180, composite values ΦˡocAB (1) = 0. 2820 versus ΦᶜollAB (1) = 0. 9146, and Landauer-deficit ratio 8. 41. Non-Markovian dynamics, feedback, and mesoscopic coarse-graining lie outside the validated core.