A Thermodynamic Criterion for Structural Persistence in Open Quantum Systems

The author introduces the Thermodynamic Criterion Index Φ_L(t) = −(dS_vN,L/dt)/σ_L(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 Φ_L = 1 − σ_irr,L/σ_L ≤ 1, with equality at the Landauer reversibility limit. The sign of Φ classifies dynamics: dissolution (Φ < 0), entropy-stationary (Φ = 0), entropy-decreasing regime (0 < Φ ≤ 1). Maximising Φ_L(t) over the flux-resolved admissible family A_aut^cut(t) = { L ∈ A_aut : σ_L(t) > σ_cut } 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 I_struct = D(ρ ∥ ρ_eq), 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 max_t [ Φ^coll_AB(t) − Φ^loc_AB(t)] = 2.3708 at t = 0.180, composite values Φ^loc_AB(1) = 0.2820 versus Φ^coll_AB(1) = 0.9146, and Landauer-deficit ratio 8.41. Non-Markovian dynamics, feedback, and mesoscopic coarse-graining lie outside the validated core.