The energetic cost of controlling a multipartite quantum system satisfies an exact sum rule: the global heat cost equals the sum of local heat costs plus temperature times the change in multipartite mutual information plus a dissipated-work contrast.
On the decrease in entropy in a thermodynamic sys- tem by the intervention of intelligent beings,
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Global-Local Duality of Energetic Control Cost in Multipartite Quantum Correlated Systems
The energetic cost of controlling a multipartite quantum system satisfies an exact sum rule: the global heat cost equals the sum of local heat costs plus temperature times the change in multipartite mutual information plus a dissipated-work contrast.