  The Carnot statement of the second law of thermodynamics poses an upper limit
on the efficiency of all heat engines. Recently, it has been studied whether
generic quantum features such as coherence and quantum entanglement could allow
for quantum devices with efficiencies larger than the Carnot efficiency. The
present study shows that this is not permitted by the laws of thermodynamics.
In particular, we will show that rather the definition of heat has to be
modified to account for the thermodynamic cost for maintaining coherence and
entanglement. Our theoretical findings are numerically illustrated for an
experimentally relevant example from optomechanics.
