  We study the statistics of the efficiency in a class of isothermal cyclic
machines with realistic coupling between the internal degrees of freedom. We
derive, under fairly general assumptions, the probability distribution function
for the efficiency. We find that the macroscopic efficiency is always equal to
the most likely efficiency, and it lies in an interval whose boundaries are
universal as they only depend on the input and output thermodynamic forces, and
not on the details of the machine. The machine achieves the upper boundary of
such an interval only in the limit of tight coupling. Furthermore, we find that
the tight coupling limit is a necessary, yet not sufficient, condition for the
engine to perform close to the reversible efficiency. The reversible efficiency
is the least likely regardless of the coupling strength, in agreement with
previous studies. By using a large deviation formalism we derive a fluctuation
relation for the efficiency which holds for any number of internal degrees of
freedom in the system.
