2015/03/29 by X. San Liang, Liang, X. San · 4 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · #Cellular Automata and Applications #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Gene Regulatory Network Analysis #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.1503.08389
openalex publication_date 2015/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Information flow (or information transfer as may be called) the widely applicable general physics notion can be rigorously derived from first principles, rather than axiomatically proposed as an ansatz. Its logical association with causality and, particularly, the most stringent one-way causality, if existing, is firmly substantiated and stated as a fact in proved theorems. Established in this study are the information flows among the components of time-discrete mappings and time-continuous dynamical systems of arbitrary dimensionality, both deterministic and stochastic. They have been obtained explicitly in closed form, and all possess the property of causality, which reads: if a component, say xi, has an evolutionary law independent of xj, then the information flow from xj to xi vanishes. These results have been put to applications with benchmark systems, such as the Kaplan-Yorke map, the Rössler system, the baker transformation, the Hénon map, and a stochastic potential flow. Besides recovering the properties as expected from the respective systems, some of the applications show that the information flow structure underlying a complex trajectory pattern could be tractable. For linear systems, the resulting remarkably concise formula asserts analytically that causation implies correlation, while correlation does not imply causation, resolving unambiguously the long-standing debate over causation versus correlation.