Zanin Massimiliano, Papo David
Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain.
Department of Neuroscience and Rehabilitation, Section of Physiology, University of Ferrara, 44121 Ferrara, Italy.
Entropy (Basel). 2021 Nov 8;23(11):1474. doi: 10.3390/e23111474.
The assessment of time irreversibility, i.e., of the lack of invariance of the statistical properties of a system under the operation of time reversal, is a topic steadily gaining attention within the research community. Irreversible dynamics have been found in many real-world systems, with alterations being connected to, for instance, pathologies in the human brain, heart and gait, or to inefficiencies in financial markets. Assessing irreversibility in time series is not an easy task, due to its many aetiologies and to the different ways it manifests in data. It is thus not surprising that several numerical methods have been proposed in the last decades, based on different principles and with different applications in mind. In this contribution we review the most important algorithmic solutions that have been proposed to test the irreversibility of time series, their underlying hypotheses, computational and practical limitations, and their comparative performance. We further provide an open-source software library that includes all tests here considered. As a final point, we show that "one size does not fit all", as tests yield complementary, and sometimes conflicting views to the problem; and discuss some future research avenues.
对时间不可逆性的评估，即对系统在时间反演操作下统计特性缺乏不变性的评估，是一个在研究界日益受到关注的话题。在许多现实世界的系统中都发现了不可逆动力学，其变化与例如人类大脑、心脏和步态中的病变，或金融市场中的低效率有关。评估时间序列中的不可逆性并非易事，这是由于其病因众多，且在数据中的表现方式各异。因此，在过去几十年中基于不同原理并考虑到不同应用提出了几种数值方法也就不足为奇了。在本论文中，我们回顾了为测试时间序列的不可逆性而提出的最重要的算法解决方案、它们的基本假设、计算和实际局限性以及它们的比较性能。我们还提供了一个开源软件库，其中包括这里考虑的所有测试。最后，我们表明“一刀切并不适用”，因为不同测试对该问题会产生互补的，有时甚至相互冲突的观点；并讨论了一些未来的研究方向。
