Eur. Phys. J. E (2013) 36: 131
https://doi.org/10.1140/epje/i2013-13131-y

Regular Article

Compressibility and pressure correlations in isotropic solids and fluids

¹ Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034, Strasbourg Cedex, France
² Institut Jean Barriol, Université de Lorraine & CNRS, 1 bd Arago, 57078, Metz Cedex 03, France
³ FMF, University of Freiburg, Stefan-Meier-Str. 21, D-79104, Freiburg, Germany
⁴ Theoretical Polymer Physics, University of Freiburg, Hermann-Herder-Str. 3, D-79104, Freiburg, Germany

^* e-mail: joachim.wittmer@ics-cnrs.unistra.fr

Received: 12 June 2013
Revised: 22 October 2013
Accepted: 12 November 2013
Published online: 22 November 2013

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 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 also in the NPT-ensemble where 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 .