The virial expansion is a series expansion used in statistical mechanics and thermodynamics to describe the behavior of gases. It relates the pressure of a gas to its density and temperature through a power series in density. The significance of the virial expansion lies in its ability to account for interactions between particles in a gas, which are not considered in the ideal gas law.
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The virial expansion expresses the free energy or pressure of a dilute system as a power series in number density whose coefficients encode few-body interactions.