Fluctuations of non-ergodic stochastic processes

We investigate the standard deviation δ v ( Δ t ) of the variance v [ x ] of time series x measured over a finite sampling time Δ t 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 average...

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Bibliographic Details
Published in:The European physical journal. E, Soft matter and biological physics Soft matter and biological physics, 2021, Vol.44 (4), p.54-54, Article 54
Main Authors: George, G., Klochko, L., Semenov, A. N., Baschnagel, J., Wittmer, J. P.
Format: Article
Language:English
Subjects:
Basins
Biological and Medical Physics
Biophysics
Complex Fluids and Microfluidics
Complex Systems
Condensed matter physics
Configuration management
Ergodic processes
Low temperature
Nanotechnology
Physics
Physics and Astronomy
Polymer films
Polymer Sciences
Regular Article - Flowing Matter
Soft and Granular Matter
Stochastic processes
Surfaces and Interfaces
Thin Films
Time measurement
Time series
Variance
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Summary:We investigate the standard deviation δ v ( Δ t ) of the variance v [ x ] of time series x measured over a finite sampling time Δ t 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 v [ x ck ] must be distinguished: the total variance δ v tot 2 = δ v int 2 + δ v ext 2 and its contributions δ v int 2 , the typical internal variance within the meta-basins, and δ v ext 2 , 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 δ v int and δ v ext are manifested by their different system-size dependences. Graphic abstract
ISSN:1292-8941
1292-895X
DOI:10.1140/epje/s10189-021-00070-5