  The shear stress relaxation modulus $G(t)$ may be determined from the shear
stress $\tau(t)$ after switching on a tiny step strain $\gamma$ or by inverse
Fourier transformation of the storage modulus $G^{\prime}(\omega)$ or the loss
modulus $G^{\prime\prime}(\omega)$ obtained in a standard oscillatory shear
experiment at angular frequency $\omega$. It is widely assumed that $G(t)$ is
equivalent in general to the equilibrium stress autocorrelation function $C(t)
= \beta V \langle \delta \tau(t) \delta \tau(0)\rangle$ which may be readily
computed in computer simulations ($\beta$ being the inverse temperature and $V$
the volume). Focusing on isotropic solids formed by permanent spring networks
we show theoretically by means of the fluctuation-dissipation theorem and
computationally by molecular dynamics simulation that in general $G(t) = G_{eq}
+ C(t)$ for $t > 0$ with $G_{eq}$ being the static equilibrium shear modulus. A
similar relation holds for $G^{\prime}(\omega)$. $G(t)$ and $C(t)$ must thus
become different for a solid body and it is impossible to obtain $G_{eq}$
directly from $C(t)$.
