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
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