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Compression modulus K computed using the rescaled volume fluctuations K vol| P (filled spheres), the Rowlinson stress fluctuation formula K row| V (crosses), the difference between the total pressure fluctuations in both ensembles (squares) and the fluctuations of the inverse volume (large spheres). (Main panel) The upper data refer to systems of glass-forming 2D pLJ beads at P = 2, 9 the lower data to simple 1D nets of harmonic springs at P = 0. (Inset) Compression modulus K vs. polydispersity δk of the spring constants for 1D nets with T = 0.01 and P = 0.
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Characterization of stress fluctuations in the NPT-ensemble. Large spheres refer to 2D pLJ beads for P = 2, all other symbols to 1D nets for different δk and P as indicated. (Main panel) Rescaled Rowlinson formula K row| P /P id as a function of the reduced ideal pressure x = P id/K. The bold line represents our key prediction, Eq. (3) , on which all data points collapse. (Inset) Similar scaling for the reduced correlation function ηmix| P /P id confirming Eq. (12) .
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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.
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