G. Röpke
Expressions for the thermodynamic and transport properties of plasmas are derived from quantum statistics in the form of equilibrium correlation functions. These can be evaluated using analytical methods or numerical approaches such as DFT-MD and PIMC simulations. Virial expansions are obtained using the Green's function method. They provide benchmarks for numerical simulations and are useful in the low-density range. The results for the equation of state are discussed for the uniform electron gas and the hydrogen plasma. Transport properties such as the dielectric function are also of interest. Virial expansions are considered for the electrical direct current conductivity as a special case of the dielectric function. Examples are given, and it is explained where further work is needed to obtain a consistent description of the properties of hot and dense plasmas.