Review of the Natural Time Analysis Method and Its Applications

A new concept of time, termed natural time, was introduced in 2001. This new concept reveals unique dynamic features hidden behind time-series originating from complex systems. In particular, it was shown that the analysis of natural time enables the study of the dynamical evolution of a complex system and identifies when the system enters a critical stage. Hence, natural time plays a key role in predicting impending catastrophic events in general. Several such examples were published in a monograph in 2011, while more recent applications were compiled in the chapters of a new monograph that appeared in 2023. Here, we summarize the application of natural time analysis in various complex systems, and we review the most recent findings of natural time analysis that were not included in the previously published monographs. Specifically, we present examples of data analysis in this new time domain across diverse fields, including condensed-matter physics, geophysics, earthquakes, volcanology, atmospheric sciences, cardiology, engineering, and economics.