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.
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