The Remainder in Mayer's Fugacity Series

Upper and lower bounds are obtained for the remainder after a finite number of terms of the expansions in powers of fugacity z for the pressure p, the s-particle distribution functions, the density ρ, and the fugacity coefficient z/ρ, for a system of particles with two-body interactions. The interaction potential must be either nonnegative or else have a hard core and decrease faster than r−3 at large distances. The results hold for all positive z, and apply to lattice gases as well as to fluids. For nonnegative potentials, the results imply that successive partial sums of each of these fugacity expansions provide alternate upper and lower bounds, valid even if the series diverges, on the physical quantity the expansion represents.