Regular Article – Flowing Matter
Simple models for strictly non-ergodic stochastic processes of macroscopic systems
Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034, Strasbourg Cedex, France
Accepted: 21 September 2021
Published online: 11 October 2021
We investigate simple models for strictly non-ergodic stochastic processes (t being the discrete time step) focusing on the expectation value v and the standard deviation of the empirical variance of finite time series . is averaged over a fluctuating field ( being the microcell position) characterized by a quenched spatially correlated Gaussian field . Due to the quenched -field becomes a finite constant, , for large sampling times . The volume dependence of the non-ergodicity parameter is investigated for different spatial correlations. Models with marginally long-ranged -correlations are successfully mapped on shear stress data from simulated amorphous glasses of polydisperse beads.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2021