Frozen in time: A review of non-ergodic physical systems

The common feature of non-ergodic systems is an internal timescale that greatly exceeds the external observational timescale $t_{obs}$. This kinetic state of broken ergodicity occurs in many systems, with profound thermodynamic implications. In this work, we present a review of non-ergodic physical systems focused on the common origins of non-ergodic behavior across diverse material systems. We begin with a theoretical discussion of energy landscapes and two treatments of thermodynamics in broken ergodic systems. We then discuss several characteristic material classes that exhibit non-ergodic behavior, describing the process of ergodic breakdown and its signatures for each. The disordered nature and frustration of different energetic interactions in the example systems are discussed as the possible origin of non-ergodic dynamics. We conclude with several considerations that can assist in the identification of non-ergodic behavior. This review intends to unify the behavior of a diverse group of physical systems with a common description to aid future discussions between these fields of study.