An Exact Theory of Causal Emergence for Linear Stochastic Iteration Systems

• DOI: 10.3390/e26080618
• Publication Date: 2024-07-24T14:46:20Z
• Authors: Kaiwei Liu; Bing Yuan; Jiang Zhang
• Keywords: causal emergence; effective information; FOS: Computer and information sciences; 0303 health sciences; Science; Physics; QC1-999; Computer Science - Information Theory; Information Theory (cs.IT); Q; coarse-graining; Systems and Control (eess.SY); linear stochastic iteration system; Astrophysics; Electrical Engineering and Systems Science - Systems and Control; Article; QB460-466; 03 medical and health sciences; FOS: Electrical engineering, electronic engineering, information engineering

After coarse-graining a complex system, the dynamics of its macro-state may exhibit more pronounced causal effects than those micro-state. This phenomenon, known as emergence, is quantified by indicator effective information. However, two challenges confront this theory: absence well-developed frameworks in continuous stochastic dynamical systems and reliance on methodologies. In study, we introduce an exact theoretic framework for emergence within linear iteration featuring state spaces Gaussian noise. Building upon foundation, derive analytical expression information across general identify optimal strategies that maximize degree when dimension averaged uncertainty eliminated has upper bound. Our investigation reveals maximal methods are primarily determined principal eigenvalues eigenvectors dynamic system's parameter matrix, with latter not being unique. To validate our propositions, apply models to three simplified physical systems, comparing outcomes numerical simulations, consistently achieve congruent results.