Integrated Information, a Complexity Measure for optimal partitions

Otavio Citton; Nestor Caticha

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arXiv · 2304.14316

Integrated Information, a Complexity Measure for optimal partitions

Otavio Citton·Nestor Caticha

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Abstract

Motivated by the possible applications that a better understanding of consciousness might bring, we follow Tononi's idea and calculate analytically a complexity index for two systems of Ising spins with parallel update dynamics, the homogeneous and a modular infinite range models. Using the information geometry formulation of integrated information theory, we calculate the geometric integrated information index, $\phi_G(\Pi)$ for a fixed partition $\Pi$ with $K$ components and $\Phi=$max$_\Pi\phi_G(\Pi)$ for $K=2$ or $3$. For systems in the deep ferromagnetic phase, the optimal partition undergoes a transition such that the smallest (largest) component is above (resp. below) its critical temperature. The effects of partitioning are taken into account by introducing site dilution.

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Otavio Citton, Nestor Caticha. 2023-04-27. Integrated Information, a Complexity Measure for optimal partitions. https://arxiv.org/abs/2304.14316

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