  State-of-the-art simulations of high-energy nuclear collisions rely on hybrid
setups, involving in particular a pre-equilibrium stage to let the system
evolve from a far-from-equilibrium initial condition towards a
near-equilibrated state after which fluid dynamics can be applied meaningfully.
A known issue is the mismatch between the equation of state in the
fluid-dynamical evolution and the effective one in the previous stage, which
leads to discontinuities at the interface between the two models. Here we
introduce a new matching prescription at this interface, based on the entropy,
and we compare it with the standard one relying on local energy conservation.
We study the behavior of various quantities at the switching time between the
models and investigate a number of final-state hadronic observables. For the
latter, we show that they are not modified significantly by the choice of
matching prescription, provided an appropriate normalization is chosen for the
initial state. In turn, our approach reduces sizeably the ratio of bulk over
thermodynamic pressure at the beginning of the fluid-dynamical stage.
