Formulation of the third-order Grüneisen parameter at extreme compression

We present a direct method using the basic principles of calculus to derive the expression for the third-order Grüneisen parameter in terms of the pressure derivatives of bulk modulus at extreme compression. The derivation presented here does not depend on the assumptions regarding the values of free-volume parameter and its variation with pressure. The identities used in the present analysis are valid at extreme compression for all physically acceptable equations of state.