We investigate by means of molecular dynamics simulation a coarse-grained polymer glass model focusing on (quasistatic and dynamical) shear-stress fluctuations as a function of temperature $T$ and sampling time $\mathrm{\Delta }t$. The linear response is characterized using (ensemble-averaged) expectation values of the contributions (time averaged for each shear plane) to the stress-fluctuation relation ${\mu }_{\mathrm{sf}}$ for the shear modulus and the shear-stress relaxation modulus $G\left(t\right)$. Using 100 independent configurations, we pay attention to the respective standard deviations. While the ensemble-averaged modulus ${\mu }_{\mathrm{sf}}\left(T\right)$ decreases continuously with increasing $T$ for all $\mathrm{\Delta }t$ sampled, its standard deviation $\delta {\mu }_{\mathrm{sf}}\left(T\right)$ is nonmonotonic with a striking peak at the glass transition. The question of whether the shear modulus is continuous or has a jump singularity at the glass transition is thus ill posed. Confirming the effective time-translational invariance of our systems, the $\mathrm{\Delta }t$ dependence of ${\mu }_{\mathrm{sf}}$ and related quantities can be understood using a weighted integral over $G\left(t\right)$.

• Received 31 October 2017

DOI:https://doi.org/10.1103/PhysRevE.97.012502