2014/09/16 by Benjamin Allen, Blake C. Stacey, Allen, Benjamin +4
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Gene Regulatory Network Analysis #Origins and Evolution of Life #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1409.4708
60 pages, 10 figures
arxiv created 2014/09/16 · openalex publication_date 2014/09/16 · arxiv updated 2014/09/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information theory. In the interest of flexibility we allow information to be quantified using any function, including Shannon entropy and Kolmogorov complexity, that satisfies certain fundamental axioms. Using these axioms, we formalize the notion of a dependency among components, and show how a system's structure is revealed in the amount of information assigned to each dependency. We explore quantitative indices that summarize system structure, providing a new formal basis for the complexity profile and introducing a new index, the "marginal utility of information". Using simple examples, we show how these indices capture intuitive ideas about structure in a quantitative way. Our formalism also sheds light on a longstanding mystery: that the mutual information of three or more variables can be negative. We discuss applications to complex networks, gene regulation, the kinetic theory of fluids and multiscale cybernetic thermodynamics.