We introduce an information-theoretic method for quantifying causality in chaotic systems. The approach, referred to as IT-causality, quantifies causality by measuring the information gained about future events conditioned on the knowledge of past events. The causal interactions are classified into redundant, unique, and synergistic contributions depending on their nature. The formulation is non-intrusive, invariance under invertible transformations of the variables, and provides the missing causality due to unobserved variables. The method only requires pairs of past-future events of the quantities of interest, making it convenient for both computational simulations and experimental investigations. IT-causality is validated in four scenarios representing basic causal interactions among variables: mediator, confounder, redundant collider, and synergistic collider. The approach is leveraged to address two questions relevant to turbulence research: i) the scale locality of the energy cascade in isotropic turbulence, and ii) the interactions between inner and outer layer flow motions in wall-bounded turbulence. In the former case, we demonstrate that causality in the energy cascade flows sequentially from larger to smaller scales without requiring intermediate scales. Conversely, the flow of information from small to large scales is shown to be redundant. In the second problem, we observe a unidirectional causality flow, with causality predominantly originating from the outer layer and propagating towards the inner layer, but not vice versa. The decomposition of IT-causality into intensities also reveals that the causality is primarily associated with high-velocity streaks.

翻译：本文提出了一种用于量化混沌系统中因果性的信息论方法，称为IT-因果性。该方法通过测量基于过去事件知识条件下未来事件所获得的信息来量化因果性。根据因果相互作用的性质，将其分类为冗余、唯一和协同贡献。该公式具有非侵入性，在变量的可逆变换下保持不变，并能提供因未观测变量导致的缺失因果性。该方法仅需要所关注变量的过去-未来事件对，因此便于计算模拟和实验研究。IT-因果性在代表变量间基本因果相互作用的四种场景中得到了验证：中介变量、混杂变量、冗余碰撞子和协同碰撞子。该方法被用于解决湍流研究中的两个问题：(i) 各向同性湍流中能量级串的尺度局域性，以及(ii) 壁面湍流中内层与外层流动运动之间的相互作用。对于前者，我们证明了能量级串中的因果性从大尺度依次流向小尺度，无需中间尺度；相反，从小尺度到大尺度的信息流被证明是冗余的。在第二个问题中，我们观察到单向因果流，因果性主要源自外层并传播至内层，反之则不成立。将IT-因果性分解为强度值还揭示出，因果性主要与高速条带相关联。