Augmented Onsager Operator Maps Quantum Spin to Non-Dissipative Catalytic Circulation

The work applies Onsager-Casimir parity rules to catalytic interfaces, constructing the operator A = D + L from published electronic-structure data on doped carbon supports. This yields a basis-invariant Gateway number that quantifies circulation relative to dissipation, converting conventional one-dimensional volcano plots into two-dimensional activity surfaces. The approach explicitly incorporates time-reversal-odd spin coordinates that standard binding-energy descriptors omit.

Existing single-atom catalyst literature has focused on symmetric response quantities and overlooked the antisymmetric circulation that becomes measurable near spin-crossover points. By mapping Thermo-Hydro-Mechanical-Chemical-Electrical-Spin couplings via a Hasse diagram, the framework reveals how magnetic perturbations can modulate turnover without altering binding energies, a connection missed in prior density-functional studies of Fe-N-C and Co-N-C sites.

The authors propose a falsifiable test: apply modulated magnetic fields across a spin-crossover transition while measuring faradaic efficiency. Confirmation would require observing circulation-driven rate changes exceeding thermal noise within a 10 mT window, establishing spin as an independent control variable in electrocatalysis design.