Compressibility and pressure correlations in isotropic solids and fluids

Presenting simple coarse-grained models of isotropic solids and fluids in d = 1 , 2 and 3 dimensions we investigate the correlations of the instantaneous pressure and its ideal and excess contributions at either imposed pressure (NPT-ensemble, λ = 0 or volume (NVT-ensemble, λ = 1 and for more general values of the dimensionless parameter λ characterizing the constant-volume constraint. The stress fluctuation representation F(Row)|λ=1 of the compression modulus K in the NVT-ensemble is derived directly (without a microscopic displacement field) using the well-known thermodynamic transformation rules between conjugated ensembles. The transform is made manifest by computing the Rowlinson functional F(Row)| also in the NPT-ensemble where F(Row)|λ=1 = K f 0(x) with x = P id/K being a scaling variable, P id the ideal pressure and f 0(x) = x(2-x) a universal function. By gradually increasing λ by means of an external spring potential, the crossover between both classical ensemble limits is monitored. This demonstrates, e.g., the lever rule F(Row)|λ= K[λ = (1 - λ)f 0(x)].