Here H ( 1 , 2 , … … , n ) is the Hamiltonian (energy operator) of a subsystem of n particles. The Hamiltonian is a sum of the kinetic energies of the particles and the total n -particle potential energy (interaction energy). The latter includes pair interactions and possibly 3-body and higher-body interactions. The grand partition function Ξ Ξ can be expanded in a sum of contributions from one-body, two-body, etc. clusters. The virial expansion is obtained from this expansion by observing that ln ⁡ ⁡ Ξ Ξ equals p V / ( k B T ) . In this manner one derives