In a manner that hinders productivity or works against efficient output; in a counterproductive way.
Adverbial form of antiproductive. Formed using the -ly suffix added to antiproductive in 20th-century English as the adjective form became established.
When someone describes a system working 'antiproductively,' they're making a precise measurement claim—that the mechanism actually decreases overall output rather than increasing it, making it worse than doing nothing.
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