Wittmer J P, Xu H, Polińska P, Gillig C, Helfferich J, Weysser F, Baschnagel J
Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034, Strasbourg Cedex, France,
Eur Phys J E Soft Matter. 2013 Nov;36(11):131. doi: 10.1140/epje/i2013-13131-y. Epub 2013 Nov 22.
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 F(Row)|λ=1 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 F(Row)| also in the NPT-ensemble where F(Row)|λ=1 = K f 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 F(Row)|λ= K[λ = (1 - λ)f 0(x)].
通过给出一维、二维和三维各向同性固体和流体的简单粗粒化模型，我们研究了在施加压力（NPT系综，λ = 0）或体积（NVT系综，λ = 1）以及表征恒定体积约束的无量纲参数λ的更一般值下，瞬时压力及其理想贡献和过量贡献之间的相关性。利用共轭系综之间著名的热力学变换规则，直接（无需微观位移场）推导了NVT系综中压缩模量K的应力涨落表示F(Row)|λ=1。通过在NPT系综中计算Rowlinson泛函F(Row)|，该变换得以体现，其中F(Row)|λ=1 = K f 0(x)，x = P id/K为标度变量，P id为理想压力，f 0(x) = x(2 - x)为通用函数。通过借助外部弹簧势逐渐增加λ，监测两个经典系综极限之间的转变。例如，这证明了杠杆规则F(Row)|λ= K[λ = (1 - λ)f 0(x)]。
