Spectroscopic classification of non-ergodic populations

Non-ergodicity impacts statistical inference in a diverse range of disciplines inside and outside of physics. However the concept of ergodicity is used inconsistently, and may refer to several nonequivalent notions. To help address this, we first identify and clarify the relationship between three major interpretations of ergodicity. We then introduce a method of spectral analysis of non-ergodicity which may be performed using data alone, and so may be applied in both numerical and empirical contexts. This may be used to identify, quantify, and classify non-ergodic populations within an ergodic decomposition. This is demonstrated with an application to the Kob-Andersen kinetically constrained lattice glass model.