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maximum in T$_{xx}$ ( x ), leading the response of T$_{yy}$ and roughly equal in magnitude to that found in the dynamical results of Section II. 

The physical ideas incorporated in this simplest approach are four: (i) the pressure and the work done can usefully be separated into a “cold” part and a “thermal” part; (ii) the heat flux Q responds to a linear combination of the temperature gradients ∇ T$_{xx}$ and ∇ T$_{yy}$ in the usual way, supplemented by (iii) the thermal relaxation of the thermal anisotropicity, and (iv) separate linear combinations of the work done and heat absorbed contribute to T$_{xx}$ and T$_{yy}$ throughout the shock compression process. 

Here the total pressure, P = P Φ + P $^{K}$, contains potential and kinetic components, measurable separately with molecular dynamics. These extensions of the Navier-Stokes approach closely parallel the relaxation-time treatments of strong ideal-gas shockwaves carried out by Xu, Josyula, Holian, and Mareschal $^{11,14}$. Our more general approach necessarily differs from theirs by allowing for contributions from the potential energy to temperature changes and the transfer of heat. The pressure profiles shown in Figures 7 and 8 also indicate the need for bulk viscosity, in that the molecular dynamics results show a monotone-increasing P$_{yy}$ , in contrast to the distinct minimum found here in the absence of bulk viscosity. We turn next to a slightly more sophisticated model, an extension of Gr¨ uneisen’s equilibrium equation of state. 

