  We present a mean-field model of the dense nuclear matter equation of state
designed for use in computationally demanding hadronic transport simulations.
Our approach, based on the relativistic Landau Fermi-liquid theory, allows us
to construct a family of equations of state spanning a wide range of possible
bulk properties of dense QCD matter. We implement the developed model in the
hadronic transport code SMASH, and show that the resulting dynamic behavior
reproduces theoretical expectations for the thermodynamic properties of the
system based on the underlying equation of state. In particular, we show that
pair distribution functions calculated from hadronic transport simulation data
are consistent with theoretical expectations based on the second-order cumulant
ratio, and can be used as a signature of crossing the phase diagram in the
vicinity of a critical point. We additionally present a novel method that may
enable a measurement of the speed of sound and its derivative with respect to
the baryon number density in heavy-ion collisions. Application of our approach
to available experimental data implies that the derivative of the speed of
sound is non-monotonic in systems created in collisions at intermediate to low
energies, which in turn may be connected to non-trivial features in the
underlying equation of state.
