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We introduce an information-theoretic method for quantifying causality inchaotic systems. The approach, referred to as IT-causality, quantifiescausality by measuring the information gained about future events conditionedon the knowledge of past events. The causal interactions are classified intoredundant, unique, and synergistic contributions depending on their nature. Theformulation is non-intrusive, invariance under invertible transformations ofthe variables, and provides the missing causality due to unobserved variables.The method only requires pairs of past-future events of the quantities ofinterest, making it convenient for both computational simulations andexperimental investigations. IT-causality is validated in four scenariosrepresenting basic causal interactions among variables: mediator, confounder,redundant collider, and synergistic collider. The approach is leveraged toaddress two questions relevant to turbulence research: i) the scale locality ofthe energy cascade in isotropic turbulence, and ii) the interactions betweeninner and outer layer flow motions in wall-bounded turbulence. In the formercase, we demonstrate that causality in the energy cascade flows sequentiallyfrom larger to smaller scales without requiring intermediate scales.Conversely, the flow of information from small to large scales is shown to beredundant. In the second problem, we observe a unidirectional causality flow,with causality predominantly originating from the outer layer and propagatingtowards the inner layer, but not vice versa. The decomposition of IT-causalityinto intensities also reveals that the causality is primarily associated withhigh-velocity streaks.

Information-theoretic causality and applications to turbulence: energy cascade and inner/outer layer interactions