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Ergodicity Breaking in a Deterministic Dynamical System

Golan Bel·Eli Barkai
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Abstract

The concept of weak ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak ergodicity breaking describes a weakly chaotic dynamical system: a nonlinear map which generates subdiffusion deterministically. In the non-ergodic phase non-trivial distribution of the fraction of occupation times is obtained. The visitation fraction remains uniform even in the non-ergodic phase. In this sense the non-ergodicity is quantified, leading to a statistical mechanical description of the system even though it is not ergodic.

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Golan Bel, Eli Barkai. 2006-11-07. Ergodicity Breaking in a Deterministic Dynamical System. https://doi.org/10.1209/epl%2Fi2005-10501-8

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