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We analyzed the variance of time series in non-ergodic systems, distinguishing variances within and between meta-basins. The order of averaging impacts results, with distinct system-size dependencies observed.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Non-ergodic systems exhibit complex dynamics due to meta-basins.
  • The order of averaging (time vs. configuration) is crucial for analyzing time series data.
  • Understanding variance in such systems is key to characterizing their behavior.

Purpose of the Study:

  • To investigate the standard deviation of the variance of time series in non-ergodic systems.
  • To differentiate and analyze contributions to total variance from internal and inter-basin dynamics.
  • To explore how averaging order affects statistical properties.

Main Methods:

  • Analysis of time series variance over finite sampling times.
  • Distinguishing three types of variance: total, internal, and inter-basin.
  • Considering simplifications for systems with stochastic variables from averaged density fields.

Main Results:

  • Identified three distinct variances: total variance, internal variance within meta-basins, and dispersion between basins.
  • Demonstrated that the order of averaging configurations and time series affects the observed variances.
  • Observed different system-size dependencies for the internal and inter-basin variances.

Conclusions:

  • The statistical properties of time series variance in non-ergodic systems depend on the averaging procedure.
  • The distinction between internal and inter-basin variances provides deeper insight into system dynamics.
  • Observed system-size dependencies offer a way to experimentally differentiate these statistical measures.