  We investigate the microscopic features of bosonic quantum transport in a
non-equilibrium steady state, which breaks time reversal invariance
spontaneously. The analysis is based on the probability distributions,
generated by the correlation functions of the particle current and the entropy
production operator. The general approach is applied to an exactly solvable
model with a point-like interaction driving the system away from equilibrium.
The quantum fluctuations of the particle current and the entropy production are
explicitly evaluated in the zero frequency limit. It is shown that all moments
of the entropy production distribution are non-negative, which provides a
microscopic version of the second law of thermodynamics. On this basis a
concept of efficiency, taking into account all quantum fluctuations, is
proposed and analysed. The role of the quantum statistics in this context is
also discussed.
