  We use a one-dimensional (1d) core-softened potential to develop a physical
picture for some of the anomalies present in liquid water. The core-softened
potential mimics the effect of hydrogen bonding. The interest in the 1d system
stems from the facts that closed-form results are possible and that the
qualitative behavior in 1d is reproduced in the liquid phase for higher
dimensions. We discuss the relation between the shape of the potential and the
density anomaly, and we study the entropy anomaly resulting from the density
anomaly. We find that certain forms of the two-step square well potential lead
to the existence at T=0 of a low-density phase favored at low pressures and of
a high-density phase favored at high pressures, and to the appearance of a
point $C'$ at a positive pressure, which is the analog of the T=0 ``critical
point'' in the $1d$ Ising model. The existence of point $C'$ leads to anomalous
behavior of the isothermal compressibility $K_T$ and the isobaric specific heat
$C_P$.
