Non-additive divergences yield explicit catalyst corrections in quantum thermodynamic second laws and show that reduced-state monotones are insufficient to characterize accessibility in correlated catalysis.
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An antisymmetric integer-transfer operator on quantized states realizes exact discrete conservation for scalar and system conservation laws while selecting admissible shocks via monotone transfers.
Asymmetric well widths and barrier in a bistable potential allow finite-time bit erasure with heat below kT ln 2, bounded below by the effective free-energy change of the process.
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