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Pressure fluctuations in isotropic solids and fluids

Comparing isotropic solids and fluids at either imposed volume or pressure we investigate various correlations of the instantaneous pressure and its ideal and excess contributions. Focusing on the compression modulus K it is emphasized that the stress fluctuation representation of the elastic moduli may be obtained directly (without a microscopic displacement field) by comparing the stress fluctuations in conjugated ensembles. This is made manifest by computing the Rowlinson stress fluctuation expression K_row of the compression modulus for NPT-ensembles. It is shown theoretically and numerically that K_row|P = P_id (2 - P_id/K) with P_id being the ideal pressure contribution.