Correlation-Powered Work: Equivalence in Peak Yield, Differences in Robustness

Initial system-environment correlations are a thermodynamic resource, enabling work extraction via their erasure. We compare the work potential of classical, quantum, and hypothetical stronger-than-quantum correlations as a function of measurement misalignment. While all models can yield a peak extractable work of k_B T ln 2, corresponding to a mutual information of ln 2, their value as a resource differs critically in its robustness. The classical resource is fragile, decaying linearly with misalignment, whereas the quantum resource is robust, decaying only quadratically. Thus, the degree of nonlocality maps not to the maximum energetic value of a correlation, but to its operational robustness as a thermodynamic fuel.