  In the description of non equilibrium situations in a superconductor at
temperatures far below its critical temperature, the Keldysh-Usadel technique
(KUT) is required. However, the non-stationary KUT has not been applied to
realistic circuits. Moreover, the stationary KUT has been applied in situations
where time independence is not guaranteed. As a plausibility check for this
procedure, we resort to a toy model (the Ginzburg-Landau model), in situations
that involve very slow evolution. We find that, even in these situations,
neglecting the explicit influence of time variation leads to inaccurate or even
qualitatively wrong description of phase slips.
