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This paper determines the excess free energy associated with the formation ofa spherical cavity in a hard sphere fluid. The solvation free energy can becalculated by integration of the structural changes induced by inserting thecavity using a number of different exact thermodynamic pathways. We considerthree such pathways, including a new density route derived here. Structuralinformation about the nonuniform hard sphere fluid in the presence of a generalexternal field is given by the recently developed hydrostatic linear response(HLR) integral equation. Use of the HLR results in the different pathways givesa generally accurate determination of the solvation free energy for cavitiesover a wide range of sizes, from zero to infinity. Results for a relatedmethod, the Gaussian Field Model, are also discussed.Comment: 10 pages, 4 figures; submitted to J. Chem. Phy

Different thermodynamic pathways to the solvation free energy of a spherical cavity in a hard sphere fluid