  The recently established connection between stochastic thermodynamics and
fluctuating hydrodynamics is applied to a study of efficiencies in the coupled
transport of heat and matter on a small scale. A stochastic model for a
mesoscopic cell connected to two macroscopic reservoirs of heat and particles
is developed, based on fluctuating hydrodynamics. Within this approach, the
fluctuating separation and thermodynamic efficiencies are defined. The
conditions required to observe bimodal distributions of these efficiencies are
determined, and the evolution of these distributions is investigated in the
large-size and in the long-time limits. The results obtained are not restricted
to thermodiffusion and can be generalized to systems where efficiency is
defined as a ratio of stochastic state variables or dissipation rates.
