  Two first-principles simulation techniques, path integral Monte Carlo (PIMC)
and density functional molecular dynamics (DFT-MD), are applied to study hot,
dense helium in the density-temperature range of 0.387 - 5.35 g/cc and 500 K -
1.28x10^8 K. One coherent equation of state (EOS) is derived by combining
DFT-MD data at lower temperatures with PIMC results at higher temperatures.
Good agreement between both techniques is found in an intermediate temperature
range. For the highest temperatures, the PIMC results converge to the
Debye-Hueckel limiting law. In order derive the entropy, a thermodynamically
consistent free energy fit is introduced that reproduces the internal energies
and pressure derived from the first-principles simulations. The equation of
state is presented in form of a table as well as a fit and is compared with
chemical models. In addition, the structure of the fluid is analyzed using pair
correlation functions. Shock Hugoniot curves are compared with recent laser
shock wave experiments.
