  The equation of state and the shock Hugoniot of deuterium are calculated
using a first-principles approach, for the conditions of the recent shock
experiments. We use density functional theory within a classical mapping of the
quantum fluids [ Phys. Rev. Letters, {\bf 84}, 959 (2000) ]. The calculated
Hugoniot is close to the Path-Integral Monte Carlo (PIMC) result. We also
consider the {\it quasi-equilibrium} two-temperature case where the Deuterons
are hotter than the electrons; the resulting quasi-equilibrium Hugoniot mimics
the laser-shock data. The increased compressibility arises from hot $D^+-e$
pairs occuring close to the zero of the electron chemical potential.

Strongly Correlated Electrons;Materials Science;Statistical Mechanics