QI
In the literature: contested
Do quantum effects let heat engines outperform classical ones?
In plain words
Engines made of a few atoms can use superposition or entanglement in their working parts. Whether this gives more power at the same efficiency than any classical engine with the same parts is disputed.
Precise statement
For heat engines with a $d$-level working medium coupled to baths at $T_h > T_c$, compare the maximal power $P$ at fixed efficiency $\eta$ (or the efficiency at maximum power) of coherent quantum cycles with the best stochastic classical engine having the same level structure, bath couplings and control constraints. Determine whether $P_{quantum} > P_{classical}$ strictly, and identify the resource responsible.
What would settle it
A proof of strict separation, or of its absence, under matched constraints, confirmed in a trapped-ion or superconducting engine.