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Under a step stress, the Maxwell spring extends immediately by ${\sigma }_0/G_0$, while the dashpot adds ${\sigma }_{0}t/\eta$. Hence $J(t)=G_0^{-1}+t/\eta$, and the microrheology of a Maxwell fluid relation givesThis idealized overdamped relation describes an elastic plateau followed by long-time diffusion. Its nonzero extrapolated intercept is not the actual displacement variance at exactly zero lag, which is zero. Inertia or fast solvent relaxation must resolve the initial rise; those processes were omitted from the ideal spring-dashpot model.

A creep experiment applies a small step of stress and holds it constant while recording strain. For $\sigma ={\sigma }_{0}H(t)$, the series spring jumps by ${\sigma }_0/G_0$ and the dashpot subsequently flows at constant rate ${\sigma }_0/\eta$. The creep compliance is thusUsing the stipulated effective stress and strain substitutions givesOn linear axes the model is a straight line of positive intercept $A=k_{B}T/(\pi a{G}_0)$ and slope $A/\tau$. On logarithmic axes it has an approximate elastic plateau for $t\ll \tau$ and slope one for $t\gg \tau$, within the time window where the continuum approximation applies. The long-time slope is $6D$ with $D=k_{B}T/(6\pi \eta a)$, agreeing with the Stokes–Einstein relation.

There is an essential zero-lag convention. A literal lag displacement $\Delta \mathbf{r}(t)=\mathbf{r}(t_0+t)-\mathbf{r}(t_0)$ has $⟨|\Delta \mathbf{r}(0){|}^2⟩=0$. The nonzero intercept above is the spring-compliance extrapolation of the idealized microrheology of a Maxwell fluid, after unresolved solvent or inertial transients. It must not be interpreted as an instantaneous finite physical displacement at exactly zero lag. The stated mesh condition motivates a continuum probe response; quantitative use is more reliable for $a\gg m$ than merely $a>m$.