https://doi.org/10.1140/epje/s10189-020-00004-7
Regular Article - Flowing Matter
Ensemble fluctuations matter for variances of macroscopic variables
Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034, Strasbourg Cedex, France
e
joachim.wittmer@ics-cnrs.unistra.fr
Received:
28
September
2020
Accepted:
14
December
2020
Published online:
8
March
2021
Extending recent work on stress fluctuations in complex fluids and amorphous solids we describe in general terms the ensemble average 
and the standard deviation 
of the variance 
of time series 
of a stochastic process x(t) measured over a finite sampling time 
. Assuming a stationary, Gaussian and ergodic process, 
is given by a functional 
of the autocorrelation function h(t). is shown to become large and similar to if corresponds to a fast relaxation process. Albeit 
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.
© EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2021
