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This study explores weak ergodicity breaking in random walks with global memory. Researchers found that global memory effects can cause ergodicity breaking without needing power-law statistics.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems

Background:

  • Ergodicity breaking describes systems where time averages diverge from ensemble averages.
  • Random walks with memory exhibit complex dynamics influenced by their history.

Purpose of the Study:

  • To investigate weak ergodicity breaking in globally correlated random walks.
  • To identify mechanisms of ergodicity breaking beyond traditional power-law statistics.

Main Methods:

  • Analysis of random walk dynamics with state-dependent waiting time distributions.
  • Derivation of probability density for time-averaged observables.
  • Comparison of time and ensemble averages under global memory effects.

Main Results:

  • Global memory effects were shown to induce departures between time and ensemble averages.
  • Ergodicity breaking was demonstrated to occur even when mean residence times are finite.
  • The study identified global memory as an alternative mechanism for ergodicity breaking.

Conclusions:

  • Global memory effects provide a novel pathway to ergodicity breaking.
  • Power-law statistics are not a prerequisite for ergodicity breaking in these systems.
  • Analytical and numerical findings support the proposed mechanism.