Which mechanism underlies the water-like anomalies in core-softened potentials?

Using molecular dynamics simulations we investigate the thermodynamic of particles interacting with a continuous and a discrete versions of a core-softened (CS) intermolecular potential composed by a repulsive shoulder. Dynamic and structural properties are also analyzed by the simulations. We show that in the continuous version of the CS potential the density at constant pressure has a maximum for a certain temperature. Similarly the diffusion constant, $D$, at a constant temperature has a maximum at a density $\rho_{\mathrm{max}}$ and a minimum at a density $\rho_{\mathrm{min}}<\rho_{\mathrm{max}}$, and structural properties are also anomalous. For the discrete CS potential none of these anomalies are observed. The absence of anomalies in the discrete case and its presence in the continuous CS potential are discussed in the framework of the excess entropy.