https://doi.org/10.1140/epje/s10189-021-00070-5
Regular Article - Flowing Matter
Fluctuations of non-ergodic stochastic processes
Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034, Strasbourg Cedex, France
e
joachim.wittmer@ics-cnrs.unistra.fr
Received:
13
January
2021
Accepted:
8
April
2021
Published online:
18
April
2021
We investigate the standard deviation 
of the variance 
of time series 
measured over a finite sampling time 
focusing on non-ergodic systems where independent “configurations” c get trapped in meta-basins of a generalized phase space. It is thus relevant in which order averages over the configurations c and over time series k of a configuration c are performed. Three variances of 
must be distinguished: the total variance 
and its contributions 
, the typical internal variance within the meta-basins, and 
, characterizing the dispersion between the different basins. We discuss simplifications for physical systems where the stochastic variable x(t) is due to a density field averaged over a large system volume V. The relations are illustrated for the shear-stress fluctuations in quenched elastic networks and low-temperature glasses formed by polydisperse particles and free-standing polymer films. The different statistics of 
and 
are manifested by their different system-size dependences.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2021
