  Quantum systems strongly coupled to many-body systems equilibrate to the
reduced state of a global thermal state, deviating from the local thermal state
of the system as it occurs in the weak-coupling limit. Taking this insight as a
starting point, we study the thermodynamics of systems strongly coupled to
thermal baths. First, we provide strong-coupling corrections to the second law
applicable to general systems in three of its different readings: As a
statement of maximal extractable work, on heat dissipation, and bound to the
Carnot efficiency. These corrections become relevant for small quantum systems
and always vanish in first order in the interaction strength. We then move to
the question of power of heat engines, obtaining a bound on the power
enhancement due to strong coupling. Our results are exemplified on the
paradigmatic situation of non-Markovian quantum Brownian motion.
