And there's an open python repo with really clear and easy to read and code implementing the key methods:
github.com/KieranOwens/...

Take a look?! 👀

Kieran explains how all the methods can be understood through these conceptual groupings, derives new relationships between existing methods, and provides some case-study demonstrations/comparisons of how insanely well they can work on data

These powerful methods are underappreciated: A recent review of the field included *0* methods designed for time-series data, instead focusing on generic dimension reduction methods.

This paper assembles a diversity of >60 scientific methods for the first time, and unifies them across 7 categories.

If you're interested in the statistics of time-irreversibility, and how they could be used to capture novel, interpretable properties from real-world time series, take a look:
arxiv.org/abs/2511.15991
(Code here: github.com/DynamicsAndN...)

The breath of comparison (of both methods and processes) also allowed us to demonstrate that all tested indices of irreversibility had weaknesses: i.e., we could always find an irreversibile process on which any given irreverisbility index will fail to detect irreversibility.

We found key families of algorithmic constructions that were could accurately index irreversibility: (i) generalized autocorrelation functions; (ii) symbolic sequences; and (iii) forecasting-derived metrics. Some recapitulate concepts studied previously but in isolation; others are novel directions

He we compared >6000 time-series metrics to index time reversibility from simulations of 35 different reversible and irreversible processes

Quantifying time reversibility from data is important because it connects to concepts in thermodynamics (entropy production of non-equilibrium systems) & constrains the system's generative mechanisms (by ruling out linear dynamics; cf. related concepts of non-Gaussianity & nonlinearity)