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, lambda = 0 or volume (NVT-ensemble, lambda = 1 and for more general values of the dimensionless parameter lambda characterizing the constant-volume constraint. The stress fluctuation representation 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 also in the NPT-ensemble where 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 lambda 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 vertical bar(lambda) - K[lambda + (1 - lambda)f(0)(x)].