Ensemble fluctuations matter for variances of macroscopic variables.

Extending recent work on stress fluctuations in complex fluids and amorphous solids we describe in general terms the ensemble average [Formula: see text] and the standard deviation [Formula: see text] of the variance [Formula: see text] of time series [Formula: see text] of a stochastic process x(t) measured over a finite sampling time [Formula: see text]. Assuming a stationary, Gaussian and ergodic process, [Formula: see text] is given by a functional [Formula: see text] of the autocorrelation function h(t). [Formula: see text] is shown to become large and similar to [Formula: see text] if [Formula: see text] corresponds to a fast relaxation process. Albeit [Formula: see text] does not hold in general for non-ergodic systems, the deviations for common systems with many microstates are merely finite-size corrections. Various issues are illustrated for shear-stress fluctuations in simple coarse-grained model systems.