The equation of state.

There are two basic approaches to the equation of state for stellar envelopes and interiors. The traditional method chooses the so-called "chemical picture", in which the notion of atoms is maintained despite the plasma environment. A mixture of atoms, molecules, ions, electrons and nuclei is considered, and the occurring ionization and dissociation reactions (thus the name chemical picture) are treated according to the entropy-maximum (or free-energy-minimum) principle. The alternative method is based on the so-called "physical picture", where only fundamental particles (electrons, nuclei) explicitly enter. Through the means of activity expansions, the problems of plasma physics and statistical mechanics are treated simultaneously and on the same footing. For helio- and asteroseismology, an accurate and precise equation of state is essential. Progress towards a better equation of state can be made in several ways: purely theoretical efforts, checks with experiments, including astrophysical data, and comparisons between different theoretical formalisms. Comparisons are useful to assess the domain of temperature and density where the theoretical complications matter, and to determine the diagnostic potential of astrophysical observables for equation of state issues.