  We investigate the limitations that emerge in thermodynamic tasks as a result
of having local control only over the components of a thermal machine. These
limitations are particularly relevant for devices composed of interacting
many-body systems. Specifically, we study protocols of work extraction that
employ a many-body system as a working medium whose evolution can be driven by
tuning the on-site Hamiltonian terms. This provides a restricted set of
thermodynamic operations, giving rise to novel bounds for the performance of
engines. Our findings show that those limitations in control render it in
general impossible to reach Carnot efficiency; in its extreme ramification it
can even forbid to reach a finite efficiency of work per particle. We focus on
the 1D Ising model in the thermodynamic limit as a case study. We show that in
the limit of strong interactions the ferromagnetic case becomes useless for
work extraction, while the anti-ferromagnetic improves its performance with the
strength of the couplings, reaching Carnot in the limit of arbitrary strong
interactions. Our results provide a promising connection between the study of
quantum control and thermodynamics and introduce a more realistic set of
physical operations well suited to capture current experimental scenarios.
