  The inherent structures ({\it IS}) are the local minima of the potential
energy surface or landscape, $U({\bf r})$, of an {\it N} atom system.
Stillinger has given an exact {\it IS} formulation of thermodynamics. Here the
implications for the equation of state are investigated. It is shown that the
van der Waals ({\it vdW}) equation, with density-dependent $a$ and $b$
coefficients, holds on the high-temperature plateau of the averaged {\it IS}
energy. However, an additional ``landscape'' contribution to the pressure is
found at lower $T$. The resulting extended {\it vdW} equation, unlike the
original, is capable of yielding a water-like density anomaly, flat isotherms
in the coexistence region {\it vs} {\it vdW} loops, and several other desirable
features. The plateau energy, the width of the distribution of {\it IS}, and
the ``top of the landscape'' temperature are simulated over a broad reduced
density range, $2.0 \ge \rho \ge 0.20$, in the Lennard-Jones fluid. Fits to the
data yield an explicit equation of state, which is argued to be useful at high
density; it nevertheless reproduces the known values of $a$ and $b$ at the
critical point.
