Singlet-like correlations: equal peak work, unequal robustness

Initial system–environment correlations are a thermodynamic resource, enabling work extraction through their erasure. We compare three representative singlet-like, rotationally covariant correlation laws—a local classical benchmark, the quantum cosine law and an idealized stronger-than-quantum step law—under measurement misalignment. In the binary-outcome, uniform-marginal setting, all three can attain the same peak extractable work, kBTln 2 k B T ln 2 . Their operational value differs, however, in robustness away from perfect alignment. For the chosen classical benchmark, the mutual information degrades as Θ (δ θ ln (1/δ θ )) Θ ( δ θ ln ( 1 / δ θ ) ) , whereas for the quantum cosine law it degrades as Θ (δ θ ²ln (1/δ θ )) Θ ( δ θ 2 ln ( 1 / δ θ ) ) . The stronger-than-quantum step law is perfectly flat except at a critical angle. Accordingly, the paper establishes a robustness hierarchy within this restricted comparison class , rather than a no-go theorem for all classical correlations.