Abstract
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 \(\left. {\mathcal{F}_{Row} } \right|_{\lambda = 0} = Kf_0 (x)\) 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 \(\mathcal{F}_{Row}\) also in the NPT-ensemble where \(\left. {\mathcal{F}_{Row} } \right|_{\lambda = 0} = Kf_0 (x)\) 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 \(\left. {\mathcal{F}_{Row} } \right|_\lambda = K\left[ {\lambda + (1 - \lambda )f_0 (x)} \right]\).
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Wittmer, J.P., Xu, H., Polińska, P. et al. Compressibility and pressure correlations in isotropic solids and fluids. Eur. Phys. J. E 36, 131 (2013). https://doi.org/10.1140/epje/i2013-13131-y
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DOI: https://doi.org/10.1140/epje/i2013-13131-y