Static and dynamical properties of a model glass-forming oligomer liquid are analyzed using molecular dynamics simulations. The temperature and system size effects are assessed for the affine shear modulus μA, the quasistatic shear modulus μsf (obtained using the stress-fluctuation relation), and the shear relaxation modulus G(t). It is found that while both μA and μsf are nearly independent of the system size, their variances show significant system size dependence, in particular, below the glass transition temperature Tg. It is also shown that the standard deviation of the shear modulus, δμsf(T), exhibits a pronounced peak at T ≈ Tg whose position is nearly independent of the system volume V. Moreover, the whole function δμsf(T) is nearly the same for different system sizes above the glass transition. We propose a theory which quantitatively predicts δμsf(T) at T ≳ Tg and explains both its independence of V and its peak near Tg. It is also established that below Tg the variance of the affine modulus follows the standard power law, δμA2∝1/V, while δμsf shows anomalously a slow decrease with V as δμsf2∝1/Vα with α < 1. On this basis, it is argued that the studied glass-forming systems must show long-range structural correlations in the amorphous state.

A simple and rigorous approach to obtain stress correlations in viscoelastic liquids (including supercooled liquid and equilibrium amorphous systems) is proposed. The long-range dynamical correlations of local shear stress are calculated and analyzed in 2-dimensional space. It is established how the long-range character of the stress correlations gradually emerges as the relevant dynamical correlation length l grows in time. The correlation range l is defined by momentum propagation due to acoustic waves and vorticity diffusion which are the basic mechanisms for transmission of shear stress perturbations. We obtain the general expression defining the time- and distance-dependent stress correlation tensor in terms of material functions (generalized relaxation moduli). The effect of liquid compressibility is quantitatively analyzed; it is shown to be important at large distances and/or short times. The revealed long-range stress correlation effect is shown to be dynamical in nature and unconnected with static structural correlations in liquids (correlation length ξ). Our approach is based on the assumption that ξ is small enough as reflected in weak wave-number dependencies of the generalized relaxation moduli. We provide a simple physical picture connecting the elucidated long-range fluctuation effect with anisotropic correlations of the (transient) inherent stress field, and discuss its implications.

We investigate the standard deviation δv(∆t) of the variance v[x] of time series x measured over a finite sampling time ∆t focusing on non-ergodic systems where independent "configurations" c get trapped in meta-basins of a generalized phase space. It is thus relevant in which order averages over the configurations c and over time series k of a configuration c are performed. Three variances of v[x ck ] must be distinguished: the total variance δv 2 tot = δv 2 int +δv 2 ext and its contributions δv 2 int , the typical internal variance within the meta-basins, and δv 2 ext , characterizing the dispersion between the different basins. We discuss simplifications for physical systems where the stochastic variable x(t) is due to a density field averaged over a large system volume V . The relations are illustrated for the shear-stress fluctuations in quenched elastic networks and low-temperature glasses formed by polydisperse particles and free-standing polymer films. The different statistics of δvint and δvext are manifested by their different system-size dependences.