Thermodynamic, Dynamic, Structural and Excess Entropy Anomalies for   core-softened potentials
  Using molecular dynamic simulations we study three families of continuous core-softened potentials consisting of two length scales: a shoulder scale and an attractive scale. All the families have the same slope between the two length scales but exhibit different potential energy gap between them. For each family three shoulder depths are analyzed. We show that all these systems exhibit a liquid-liquid phase transition between a high density liquid phase and a low density liquid phase ending at a critical point. The critical temperature is the same for all cases suggesting that the critical temperature is only dependent on the slope between the two scales. The critical pressure decreases with the decrease of the potential energy gap between the two scales suggesting that the pressure is responsible for forming the high density liquid. We also show, using the radial distribution function and the excess entropy analysis, that the density, the diffusion and the structural anomalies are present if particles move from the attractive scale to the shoulder scale with the increase of the temperature indicating that the anomalous behavior depends only in what happens up to the second coordination shell. 
Ney M. Barraz Jr. and Evy Salcedo and Marcia C. Barbosa
cond-mat.stat-mech