Equation of state based on the first principles.

An alternative to the well-known complete form of the Mie–Grüneisen equation of state (EOS) for water is suggested. A closed analytical description of the self-consistent EOS for an arbitrary medium based only on the first law of thermodynamics and on a new form of virial theorem is obtained. This form of the virial theorem (allowing a variable power-law exponent of the particles interaction potential) is a result of the generalization of the known method of similarity [Feynman et al., "Equation of state of elements based on the generalized Fermi–Thomas theory," Phys. Rev. 75, 1561 (1949)]. In the new EOS, the description of the internal potential energy as a solution of a nonlinear Riemann–Hopf type equation is proposed. [ABSTRACT FROM AUTHOR]