A New Look at Broken Ergodicity

Details A New Look at Broken Ergodicity A New Look at Broken Ergodicity

1994-09-28

arxiv.org/abs/adap-org/9409004v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

29 pages; special macros jnl, journals, reforder included; 3 figures obtainable by mail from first author

Scientific paper

We study the nature and mechanisms of broken ergodicity (BE) in specific random walk models corresponding to diffusion on random potential surfaces, in both one and high dimension. Using both rigorous results and nonrigorous methods, we confirm several aspects of the standard BE picture and show that others apply in one dimension, but need to be modified in higher dimensions. These latter aspects include the notions that at fixed temperature confining barriers increase logarithmically with time, that ``components'' are necessarily bounded regions of state space which depend on the observational timescale, and that the system continually revisits previously traversed regions of state space. We examine our results in the context of several experiments, and discuss some implications of our results for the dynamics of disordered and/or complex systems.

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