Compressibility and pressure correlations in isotropic solids and fluids

摘要

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=0) = 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)].