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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Different types of spatial correlation functions for non-ergodic stochastic processes of macroscopic systems
J P Wittmer1, A N Semenov2, J Baschnagel2
1Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034, Strasbourg Cedex, France. joachim.wittmer@ics-cnrs.unistra.fr.
The European Physical Journal. E, Soft Matter
|August 6, 2022
Summary
This study analyzes variances in time-averaged data for non-ergodic systems. It reveals how internal and external variances relate to local field correlations, impacting sampling time and system volume dependencies.
Area of Science:
- Statistical Mechanics
- Complex Systems Theory
- Physical Systems Analysis
Background:
- Non-ergodic macroscopic systems exhibit complex temporal dynamics.
- Time averages of time-series data are crucial for understanding system behavior.
- Total variance is decomposed into internal and external components.
Purpose of the Study:
- To re-examine variances of time averages in non-ergodic systems.
- To establish relationships between variances and correlation functions.
- To understand the influence of sampling time and system volume.
Main Methods:
- Focus on non-ergodic macroscopic systems.
- Mathematical analysis of time-series variances.
- Expression of variances as volume averages of correlation functions.
- Illustration using lattice spring models.
Main Results:
- Demonstrated that variances can be expressed as volume averages of correlation functions.
- Traced dependencies of variances on sampling time and system volume to specific correlation functions.
- Provided a framework for analyzing fluctuations in non-ergodic systems.
Conclusions:
- The study provides a deeper understanding of variance decomposition in non-ergodic systems.
- Established a link between macroscopic variances and microscopic correlation functions.
- Offers a method to analyze system dynamics influenced by sampling and volume.
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