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.
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