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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, but disappears along the isochores andisobars, while density anomaly exists along isochors. We analyze theapplicability of the Rosenfeld entropy scaling relations to this system in theregions with the water-like anomalies. It is shown that the validity of the ofRosenfeld scaling relation for the diffusion coefficient also depends on thetrajectory in the $P-\rho-T$ space along which the kinetic coefficients and theexcess entropy are calculated.

Water-like Anomalies of Core-Softened Fluids: Dependence on the Trajectories in ($P\rho T$) Space