Entropy-Informed Coherence Costs on Connectome Routing Motifs: A Markovian Reference Surface for Dephasing-Assisted Transport

Dephasing-assisted transport on structural connectomes produces a well-characterized selectivity peak at intermediate noise (the ENAQT window), but the coherence cost of that peak has not been quantified. We adapt the Santos–Céleri–Landi coherence/population entropy decomposition to sink-driven GKSL dynamics on routing motifs extracted from Human Connectome Project structural connectomes (Lausanne scale-125, N = 5 subjects, stratified by transport advantage). The coherence-loss proxy Υ = −dC/dt, where C is the relative entropy of coherence of the conditional active state, is computed across a two-dimensional (κ, ε) parameter space (21 dephasing rates × 11 disorder levels × 10 hashed seeds). The transport peak near κ ~ 1 (resolved to κ ≈ 0.95 at ε = 0 by dense re-sweep) is disorder-robust (R₀ varies less than 6% across ε ∈ [0, 5]). Coherence consumption ΔC = C(0) − C(T_end) peaks at κ ≈ 0.3–0.6, below the transport optimum, and grows with disorder at fixed transport: at κ ≈ 1 and ε = 5, ΔC reaches 0.44 versus 0.19 at ε = 0, a 2.3-fold increase for less than 6% change in R₀. This reveals a trade-off between transport and coherence cost that is invisible in the transport curve alone. Sink-drain quantities (cumulative absorbed probability, leakage, survival fraction) are algebraically determined by R₀ and carry no independent information. Small local negative excursions of Υ survive timestep refinement and define a boundary condition for stronger thermodynamic interpretations. These results provide a Markovian reference surface for non-Markovian extensions and establish that transport advantage and coherence cost occupy distinct regions of the (κ, ε) landscape on dense routing motifs.