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In the present article we carry out a molecular dynamics study of thecore-softened system and show that the existence of the water-like anomalies inthis system depends on the trajectory in $P-\rho-T$ space along which thebehavior of the system is studied. For example, diffusion and structuralanomalies are visible along isotherms as a function of density, but disappearsalong the isochores and isobars as a function of temperature. On the otherhand, the diffusion anomaly may be seen along adiabats as a function oftemperature, density and pressure. It should be noted that it may be nosignature of a particular anomaly along a particular trajectory, but theanomalous region for that particular anomaly can be defined when all possibletrajectories in the same space are examined (for example, signature ofdiffusion anomaly is evident through the crossing of different isochors.However, there is no signature of diffusion anomaly along a particularisochor). We also analyze the applicability of the Rosenfeld entropy scalingrelations to this system in the regions with the water-like anomalies. It isshown that the validity of the Rosenfeld scaling relation for the diffusioncoefficient also depends on the trajectory in the $P-\rho-T$ space along whichthe kinetic coefficients and the excess entropy are calculated.

Core-Softened System With Attraction: Trajectory Dependence of Anomalous Behavior