Unifying concepts in information-theoretic time-series analysis

TL;DR

This paper unifies key information-theoretic measures for analyzing time-series data, standardizing their definitions and visualization to improve interdisciplinary understanding and application across fields like neuroscience and physics.

Contribution

It introduces a shared semantic framework, standardized notation, and cohesive visualizations for information-theoretic time-series measures, facilitating cross-disciplinary integration.

Findings

Illustrative case study with fMRI data demonstrates measure complementarities.

Framework enhances reproducibility and methodological adoption.

Unified approach aids interdisciplinary dialogue in complex systems analysis.

Abstract

Information theory is a powerful framework for quantifying complexity, uncertainty, and dynamical structure in time-series data, with widespread applicability across disciplines such as physics, finance, and neuroscience. However, the literature on these measures remains fragmented, with domain-specific terminologies, inconsistent mathematical notation, and disparate visualization conventions that hinder interdisciplinary integration. This work addresses these challenges by unifying key information-theoretic time-series measures through shared semantic definitions, standardized mathematical notation, and cohesive visual representations. We compare these measures in terms of their theoretical foundations, computational formulations, and practical interpretability -- mapping them onto a common conceptual space through an illustrative case study with functional magnetic resonance imaging time series in the brain. This case study exemplifies the complementary insights these measures offer in characterizing the dynamics of complex neural systems, such as signal complexity and information flow. By providing a structured synthesis, our work aims to enhance interdisciplinary dialogue and methodological adoption, which is particularly critical for reproducibility and interoperability in computational neuroscience. More broadly, our framework serves as a resource for researchers seeking to navigate and apply information-theoretic time-series measures to diverse complex systems.