Second law of thermodynamics under control restrictions.The second law of thermodynamics, formulated as an ultimate bound on the maximum extractable work, has been rigorously derived in multiple scenarios.  However, the unavoidable limitations that emerge due to the lack of control on small systems are often disregarded when deriving such bounds, which is specifically important in the context of quantum thermodynamics.  In particular, contrary to the unrestricted case, we show that the optimal work extraction is not achieved by simple thermal contacts.  Our results not only generalize the second law to scenarios of practical relevance, but also take first steps in the direction of local thermodynamics.
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