1.5mu\overline{\mkern-1.5muw\mkern-1.5mu}\mkern 1.5mu} = w_{\rm s} > 1/3$ to $w = 1/3$. For example, this could happen if the stiff fluid decays into radiation at some point (which marks the end of the SD epoch) by some process characterized by a timescale much shorter than the instantaneous Hubble time at that moment.

2.  **Smooth transition.** Here the SD spoch is driven by a fluid component (typically formed by the inflaton field itself) which dominates the energy budget of the Universe and has a stiff equation of state $w_{\rm s} > 1/3$, but there is also a relatively small amount of radiation present at the end of inflation / onset of SD. The energy densities of the two components scale freely as the Universe expands, i.e. we assume no interaction between the two sectors. Due to the different scalings, as $\propto a^{-4}$ for radiation and as $\propto a^{-3(1+w_{\rm s})}$ for the stiff fluid, the radiation component eventually dominates the energy budget of the Universe. The transition from SD to RD then occurs smoothly, over a few Hubble times, as the energy density of radiation gradually overtakes that of the stiff fluid.

Since the time-dependence of the scale factor around the SD-to-RD transition 