  If the work per cycle of a quantum heat engine is averaged over an
appropriate prior distribution for an external parameter $a$, the work becomes
optimal at Curzon-Ahlborn efficiency. More general priors of the form $\Pi(a)
\propto 1/a^{\gamma}$ yield optimal work at an efficiency which stays close to
CA value, in particular near equilibrium the efficiency scales as one-half of
the Carnot value. This feature is analogous to the one recently observed in
literature for certain models of finite-time thermodynamics. Further, the use
of Bayes' theorem implies that the work estimated with posterior probabilities
also bears close analogy with the classical formula. These findings suggest
that the notion of prior information can be used to reveal thermodynamic
features in quantum systems, thus pointing to a new connection between
thermodynamic behavior and the concept of information.
