Instituto de Matemática Interdisciplinar, Departamento de Análisis Matemático y Matemáticas Aplicadas, and GISC, Universidad Complutense, Plaza de las ciencias, 3, 28040 Madrid, Spain.
Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain.
Chaos. 2023 Mar;33(3):033138. doi: 10.1063/5.0136471.
Entropy and time asymmetry are two intertwined aspects of a system's dynamics, with the production of entropy marking a clear direction in the temporal dimension. In the last few years, metrics to quantify both properties in time series have been designed around the same concept, i.e., the use of ordinal patterns. In spite of this, the relationship between these two families of metrics is yet not well understood. In this contribution, we study this problem by constructing an entropy-time asymmetry plane and evaluating it on a large set of synthetic and real-world time series. We show how the two metrics can at times behave independently, the main reason being the presence of patterns with turning points; due to this, they yield complementary information about the underlying systems, and they have different discriminating performance.
熵和时间不对称性是系统动力学的两个相互交织的方面，熵的产生标志着时间维度上的明确方向。在过去的几年中，围绕着使用有序模式这一相同概念，已经设计出了量化时间序列中这两个特性的指标。尽管如此，这两种度量之间的关系尚未得到很好的理解。在本研究中，我们通过构建一个熵-时间不对称性平面并在大量合成和真实世界的时间序列上对其进行评估来研究这个问题。我们展示了这两个度量有时如何独立地起作用，主要原因是存在具有转折点的模式；由于这种情况，它们提供了有关基础系统的互补信息，并且具有不同的判别性能。
