Ensemble fluctuations matter for variances of macroscopic variables

G George and L Klochko and AN Semenov and J Baschnagel and JP Wittmer, EUROPEAN PHYSICAL JOURNAL E, 44, 13 (2021).

DOI: 10.1140/epje/s10189-020-00004-7

Extending recent work on stress fluctuations in complex fluids and amorphous solids we describe in general terms the ensemble average v(Delta t) and the standard deviation delta v(Delta t) of the variance vx of time series x of a stochastic process x(t) measured over a finite sampling time Delta t. Assuming a stationary, Gaussian and ergodic process, delta v is given by a functional delta vGh of the autocorrelation function h(t). delta v(Delta t) is shown to become large and similar to v(Delta t) if Delta t corresponds to a fast relaxation process. Albeit delta v=delta vGh 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.

Return to Publications page