  In this work we calculate the thermodynamic properties of hydrogen-helium
plasmas with different mass fractions of helium by the direct path integral
Monte Carlo method. To avoid unphysical approximations we use the path integral
representation of the density matrix. We pay special attention to the region of
weak coupling and degeneracy and compare the results of simulation with a model
based on the chemical picture. Further with the help of calculated deuterium
isochors we compute the shock Hugoniot of deuterium. We analyze our results in
comparison with recent experimental and calculated data on the deuterium
Hugoniot.
