A fluctuation-dissipation framework derives the planar-limit Tolman length from bulk isothermal compressibility and its pressure derivative, equivalently from second and third moments of NPT volume fluctuations, yielding approximately -0.7 Å for water at 300 K.
These pressure derivatives provide the local expansion co- efficients used later when the chemical-potential equality is expanded directly in excess-pressure variables
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Fluctuation-Dissipation Framework for Size-Dependent Surface Tension
A fluctuation-dissipation framework derives the planar-limit Tolman length from bulk isothermal compressibility and its pressure derivative, equivalently from second and third moments of NPT volume fluctuations, yielding approximately -0.7 Å for water at 300 K.