Constrained Hamiltonian realizability of thermoelectric Pareto spectra at finite power in coherent tight-binding chains

We study whether power–efficiency Pareto-optimal transmission spectra for coherent thermoelectric heat engines can be represented by a finite, constrained tight-binding Hamiltonian. Reservoir occupations are treated exactly at finite voltage and temperature bias, while the scattering Hamiltonian is kept static; the results are therefore a finite-bias Landauer benchmark with frozen scattering rather than a self-consistent model of a biased interacting device. Smooth transmission targets are optimized with NSGA-II, and 30 points sampled across the Pareto front are projected onto a five-site chain with independently variable onsite energies, hoppings and lead broadenings, followed by load re-optimization. Lowand intermediate-power targets are reproduced with small transport-weighted spectral and operating-point errors, whereas a larger mismatch appears near the high-power edge as the target develops a broad near-step transmission window. A bias-profile test shows that simple potential-shift prescriptions visibly move the power–efficiency curves, identifying electrostatic self-consistency as a substantive model limitation. An auxiliary = 3–8 sharp-window test is retained only as an approximation diagnostic and is not interpreted as a universal scaling law. Coulomb blockade, Kondo correlations, self-consistent charging and microscopic phonons are outside the present model. The main result is therefore an auditable single-particle realizability map that separates spectral-target optimization from the additional constraints required for device-level thermoelectric design.