2024/02/23 by Jiang Zhang, Ruyi Tao, Zhang, Jiang +4 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Data Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Origins and Evolution of Life #Quantum Mechanics and Applications #Statistical Mechanics (cond-mat.stat-mech) #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2402.15054
openalex publication_date 2024/02/23 · openalex created_date 2024/02/27 · openalex updated_date 2026/07/28
The theory of causal emergence (CE) with effective information (EI) posits that complex systems can exhibit CE, where macro-dynamics show stronger causal effects than micro-dynamics. A key challenge of this theory is its dependence on coarse-graining method. In this paper, we introduce a fresh concept of approximate dynamical reversibility and establish a novel framework for CE based on this. By applying singular value decomposition(SVD) to Markov dynamics, we find that the essence of CE lies in the presence of redundancy, represented by the irreversible and correlated information pathways. Therefore, CE can be quantified as the potential maximal efficiency increase for dynamical reversibility or information transmission. We also demonstrate a strong correlation between the approximate dynamical reversibility and EI, establishing an equivalence between the SVD and EI maximization frameworks for quantifying CE, supported by theoretical insights and numerical examples from Boolean networks, cellular automata, and complex networks. Importantly, our SVD-based CE framework is independent of specific coarse-graining techniques and effectively captures the fundamental characteristics of the dynamics.