The virial expansion in equilibrium and nonequilibrium statistical mechanics

We consider the generalization to nonequilibrium statistical mechanics of two of Mayer's contributions to equilibrium statistical mechanics. These are (a) the virial expansion of the equilibrium properties of a gas with short-range interparticle forces, and (b) the rearrangement of this expansion for gases with weak, long-range forces in order to incorporate a collective effect—the Debye screening—leading to the Debye-Huckel theory. For short-range forces, the formal generalization of the virial expansion to nonequilibrium has to be rearranged as in (b) in order to incorporate a collective effect—the mean free path cutoff of free particle motions. For weak long-range forces a similar rearrangement has to be carried out in order to include Debye screening in nonequilibrium plasmas. This leads to a generalization of the Balescu-Guernsey-Lenard equation to spatially in-homogeneous plasmas. An interesting formal analogy between the various equilibrium and non-equilibrium expansions is discussed.