Anomalous energy flow is impossible in uncorrelated energy-conserving systems, but with multiple conserved charges, normal flow of one charge can drag another against its gradient.
Perarnau-Llobet, K
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Anomalous flow in correlated quantum systems: No-go result and multiple-charge scenario
Anomalous energy flow is impossible in uncorrelated energy-conserving systems, but with multiple conserved charges, normal flow of one charge can drag another against its gradient.