Simple-average expressions for shear-stress relaxation modulus

Focusing on isotropic elastic networks we propose a novel simple-average expression $G(t) = \mu_A - h(t)$ for the computational determination of the shear-stress relaxation modulus $G(t)$ of a classical elastic solid or fluid and its equilibrium modulus $\G_{eq} = \lim_{t \to \infty} G(t)$. Here, $\mu_A = G(0)$ characterizes the shear transformation of the system at $t=0$ and $h(t)$ the (rescaled) mean-square displacement of the instantaneous shear stress $\hat{\tau}(t)$ as a function of time $t$. While investigating sampling time effects we also discuss the related expressions in terms of shear-stress autocorrelation functions. We argue finally that our key relation may be readily adapted for more general linear response functions.