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arXiv · 2106.06511

Dynamical independence: discovering emergent macroscopic processes in complex dynamical systems

Lionel Barnett·Anil K. Seth
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Abstract

We introduce a notion of emergence for coarse-grained macroscopic variables associated with highly-multivariate microscopic dynamical processes, in the context of a coupled dynamical environment. Dynamical independence instantiates the intuition of an emergent macroscopic process as one possessing the characteristics of a dynamical system "in its own right", with its own dynamical laws distinct from those of the underlying microscopic dynamics. We quantify (departure from) dynamical independence by a transformation-invariant Shannon information-based measure of dynamical dependence. We emphasise the data-driven discovery of dynamically-independent macroscopic variables, and introduce the idea of a multiscale "emergence portrait" for complex systems. We show how dynamical dependence may be computed explicitly for linear systems via state-space modelling, in both time and frequency domains, facilitating discovery of emergent phenomena at all spatiotemporal scales. We discuss application of the state-space operationalisation to inference of the emergence portrait for neural systems from neurophysiological time-series data. We also examine dynamical independence for discrete- and continuous-time deterministic dynamics, with potential application to Hamiltonian mechanics and classical complex systems such as flocking and cellular automata.

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Lionel Barnett, Anil K. Seth. 2021-06-11. Dynamical independence: discovering emergent macroscopic processes in complex dynamical systems. https://doi.org/10.1103/physreve.108.014304

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