Equation of state theories of condensed matter up to about 10 TPa

A knowledge of the equation of state (EOS) of matter is necessary to describe the dependence of its thermodynamic properties on its microscopic internal structure. EOS data are also vital for a variety of applications, particularly those that involve numerical simulation of dynamic processes. This has motivated intense research on EOS of materials, both in experimental and theoretical areas. Various laboratories in the world are involved in the development of techniques for the generation of increasingly higher pressures using high power lasers, electric and rail guns etc. The range of these controlled dynamic pressures is currently reaching about10 TPa. On the theoretical side, the earlier empirical methods have now been replaced by sophisticated band structure calculations. In this article, we review these first principle theoretical attempts to calculate EOS over a range of densities and temperatures, where a variety of physical phenomena such as band crossings, band closures, phase transitions, nuclear and electronic thermal excitations, core ionization, liquid disorder etc. are encountered. The emphasis in this review is on shock Hugoniot equation of state theories.