  The efficiency of small thermal machines is typically a fluctuating quantity.
We here study the efficiency large deviation function of two exemplary quantum
heat engines, the harmonic oscillator and the two-level Otto cycles. While the
efficiency statistics follows the 'universal' theory of Verley et al. [Nature
Commun. 5, 4721 (2014)] for nonadiabatic driving, we find that the latter
framework does not apply in the adiabatic regime. We relate this unusual
property to the perfect anticorrelation between work output and heat input that
generically occurs in
  the broad class of scale-invariant adiabatic quantum Otto heat engines and
suppresses thermal as well as quantum fluctuations.
