  The hard sphere system plays a basic role in condensed matter physics and
related fields, and equation of state (EoS) is the ultimate solution to its
thermodynamic properties (1-3). Dozens of EoSs have been proposed since van der
Waals historic work and many reliable EoSs are available for the stable fluid
region (3). For the metstable region, all available EoSs are not accurate
enough for various applications. It has been considered impossible to develop
an analytical EoS for the entire stable and metstable region 4. By virtue of a
potential energy landscape analysis combined with the Woodcock type EoS (2,5),
here we show that a fairly simple analytical equation can be obtained to
reproduce the compressibility of the entire region with high accuracy.
Therefore, all four amorphous states of matter, gas, liquid, supercooled liquid
and glass, can be represented with a single EoS. Examples are given to show
that highly accurate EoS is necessary for applications in thermodynamic
property or liquid structure predictions. By using conventional approaches,
such as appending an attractive term of van der Waals type (6) or using the
equation within the framework of perturbation theory (1,7), it can be extended
to an EoS for various real systems, including supercooled liquids and glasses.
