Analysis of thermodynamic identities for materials under extreme compression

Some basic relationships for materials under extreme compression are analyzed with the help of the calculus of indeterminates. The analysis presented here provides an understanding of the origin of identities and constraints at infinite pressure which are satisfied by all physically acceptable equations of state. These identities involve the bulk modulus and its pressure derivatives, the Grüneisen parameter and its volume derivatives, the thermal expansivity, and the Anderson-Grüneisen parameter. The identity for the third-order Grüneisen parameter in terms of the pressure derivatives of the bulk modulus at extreme compression is valid even if the free-volume parameter changes with pressure.