Two Temperature Thermodynamics of Classical-Map Hypernetted-Chain Theory for the Warm Dense Matter Regime

Warm dense plasmas are ubiquitous in astrophysical systems, but modeling this regime is complex due to the lack of simple expansion parameters. Properly modeling the partially degenerate electron and the strongly coupled ions traditionally requires expensive simulations via Kohn-Sham molecular dynamics or path integral monte carlo. These highly accurate methods allow the extraction of transport coefficients and equations of state for practical use in hydrodynamic models of real large-scale systems.

Faster, but more approximate methods such as hypernetted-chain theory are known to model strongly coupled systems with high accuracy. The issue with warm dense matter in this case is in the modeling of quantum electrons. We investigate the semi-classical picture wherein the quantum Hamiltonian is mapped onto a classical Hamiltonian, taking advantage of the speed and accuracy of classical integral equation theory. In particular, this mapping requires an effective classical electron temperature that differs from the physical temperature. This leads to subtleties regarding the thermodynamics of two temperature systems. We demonstrate an improved method for modeling warm dense matter in this framework and compare it with well-known models such as Dharma-Wardana's CHNC model.