Causality, dynamical systems and the arrow of time

Any scientific discipline strives to explain causes of observed phenomena. Mathematically rigorous definition of causality, and its detection in experimental data, is possible in systems evolving in time and providing measurable quantities which can be registered in consecutive instants of time, and stored in datasets called time series. Modern mathematical methods based on so-called Granger causality have been applied in diverse scientific fields from economics and finance, through Earth and climate sciences to research trying to understand the human brain. Chaotic dynamical systems are mathematical models reflecting very complicated behaviour. Recently, cooperative phenomena have been observed in coupled chaotic systems due to their ability to synchronize. On the way to synchronization, the question which system influences other systems emerges. To answer this question, researches successfully applied the Granger causality methods. In a recent study we demonstrate that chaotic dynamical systems do not respect the causality principle of the effect following the cause. We explain, however, that such principle violation cannot occur in nature, due to time irreversibility of chaotic systems. The application of causality detection methods on time-reversed time series can help us to understand the mechanisms behind the experimentally observed causalities, in particular, it can help to distinguish linear transfer of time-delayed signals from nonlinear interactions. Thus we can observe nonlinear coupling in mammalian cardio-respiratory interactions, while a linear transfer explains some causalities observed in the climate system.
The study
M. Paluš, A. Krakovská, J. Jakubík, M. Chvosteková:
Causality, dynamical systems and the arrow of time, has been published in Chaos 28, 075307 (2018).