  Motivated by recent experiments we study the influence of thermal noise on
the phase slips in toroidal Bose-Einstein condensates with a rotating weak
link. We derive a generalized Arrhenius-like expression for the rate of
stochastic phase slips. We develop a method to estimate the energy barrier
separating different superflow states. The parameters at which the energy
barrier disappears agree with the critical parameters for deterministic phase
slips obtained from dynamics simulations, which confirms the validity of our
energetic analysis. We reveal that adding thermal noise lowers the phase-slip
threshold. However, the quantitative impact of the stochastic phase slips turns
out to be too small to explain the significant discrepancy between theoretical
and the experimental results.
