  Focusing on shear-stress fluctuations we investigate numerically a simple
generic model for self-assembled transient networks formed by repulsive beads
reversibly bridged by ideal springs. With $\Delta dt$ being the sampling time
and $t_*(f) \sim 1/f$ the Maxwell relaxation time (set by the spring
recombination frequency $f$) the dimensionless parameter $\Delta x = dt/t_*(f)$
is systematically scanned from the liquid limit ($\Delta dx \gg 1)$ to the
solid limit ($\Delta x \ll 1$) where the network topology is quenched and an
ensemble average over $m$ independent configurations is required. Generalizing
previous work on permanent networks it is shown that the shear-stress
relaxation modulus $G(t)$ may be efficiently determined for all $\Delta x$
using the simple-average expression $G(t) = \mu_A - h(t)$ with $\mu_A = G(0)$
characterizing the canonical-affine shear transformation of the system at $t=0$
and $h(t)$ the (rescaled) mean-square displacement of the instantaneous shear
stress as a function of time $t$. This relation is compared to the standard
expression $G(t) = C(t)$ using the (rescaled) shear-stress autocorrelation
function $C(t)$. Lower bounds for the $m$ configurations required by both
relations are given.
