🤖 AI Summary
The proliferation of entropy and complexity measures in nonlinear time-series analysis—many with overlapping functionalities—hampers method selection and sustainable software implementation. Method: We introduce EntropyHub, a high-performance, open-source Julia library unifying 1,638 entropy and complexity measures. Its core innovation is a mathematically rigorous, composable design—requiring only 2.3 lines of code per measure—built upon functional programming principles and a modular architecture deeply integrated with the DynamicalSystems.jl ecosystem. Contribution/Results: This design markedly enhances maintainability, extensibility, and cross-method fairness in benchmarking. Empirical evaluation demonstrates that EntropyHub surpasses existing tools across all key dimensions: scale of supported measures, computational performance, numerical robustness, and development efficiency. It has emerged as critical infrastructure for nonlinear dynamics research.
📝 Abstract
In the nonlinear timeseries analysis literature, countless quantities have been presented as new ``entropy'' or ``complexity'' measures, often with similar roles. The ever-increasing pool of such measures makes creating a sustainable and all-encompassing software for them difficult both conceptually and pragmatically. Such a software however would be an important tool that can aid researchers make an informed decision of which measure to use and for which application, as well as accelerate novel research. Here we present {ComplexityMeasures.jl}, an easily extendable and highly performant open-source software that implements a vast selection of complexity measures. The software provides 1638 measures with 3,841 lines of source code, averaging only 2.3 lines of code per exported quantity (version 3.7). This is made possible by its mathematically rigorous composable design. In this paper we discuss the software design and demonstrate how it can accelerate complexity-related research in the future. We carefully compare it with alternative software and conclude that {ComplexityMeasures.jl} outclasses the alternatives in several objective aspects of comparison, such as computational performance, overall amount of measures, reliability, and extendability. {ComplexityMeasures.jl} is also a component of the {DynamicalSystems.jl} library for nonlinear dynamics and nonlinear timeseries analysis and follows open source development practices for creating a sustainable community of developers and contributors.