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- W1977583218 abstract "The cluster-star equations are inverted. These equations, Eq. (2.1), define a set of cluster functions Um in terms of star functions Vn for 2 ≤ n ≤ m. The inversion, Eq. (2.2) gives the Vn in terms of the Um; 2 ≤ m ≤ n. The cluster-star inversion yields the coefficients βn that appear in the number-density expansion of the logarithm of the grand partition function Ξ of a statistical mechanical system in terms of the coefficients bn that appear in its fugacity expansion, even when the system is in the presence of an external field. In the course of obtaining the inversion, an expression for the work necessary to bring a particle from infinity to a point r inside a classical system at equilibrium is obtained in terms of the Vm and the one-particle distribution function ρ(r), and also in terms of the Um and ρ. The expression in terms of the Vm and ρ has been previously derived by others with restrictions on the form of the potential energy; the alternative expression in terms of the Um seems to be new. Operators with essentially the same algebraic structure as the Vm appear in a recently considered asymptotic expansion of the distribution functions of a nonequilibrium system. The cluster-star inversion facilitates the determination of these operators in terms of the solution operators of the n-body Liouville equation, n ≥ 2." @default.
- W1977583218 created "2016-06-24" @default.
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- W1977583218 date "1965-08-01" @default.
- W1977583218 modified "2023-09-26" @default.
- W1977583218 title "Cluster‐Star Inversion by Means of Generating Functionals" @default.
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- W1977583218 doi "https://doi.org/10.1063/1.1704759" @default.
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