  We derive the statistics of the efficiency under the assumption that
thermodynamic fluxes fluctuate with normal law, parametrizing it in terms of
time, macroscopic efficiency, and a coupling parameter $\zeta$. It has a
peculiar behavior: No moments, one sub- and one super-Carnot maxima
corresponding to reverse operating regimes (engine/pump), the most probable
efficiency decreasing in time. The limit $\zeta\to 0$ where the Carnot bound
can be saturated gives rise to two extreme situations, one where the machine
works at its macroscopic efficiency, with Carnot limit corresponding to no
entropy production, and one where for a transient time scaling like $1/\zeta$
microscopic fluctuations are enhanced in such a way that the most probable
efficiency approaches Carnot at finite entropy production.
