An open-source toolkit for entropic data analysis


Available in:

Matlab // Python // Julia


This toolkit provides a wide range of functions to calculate different entropy statistics.
There is an ever-growing range of information-theoretic and dynamical systems entropy measures presented in the scientific literature.
The goal of EntropyHub is to integrate the many established entropy methods in one open-source package.


Information and uncertainty can be regarded as two sides of the same coin: the more uncertainty there is, the more information we gain by removing that uncertainty. In the context of dynamical systems and information theory, Entropy quantifies that uncertainty.

In the context of nonlinear dynamics, entropy is central in quantifying the degree of uncertainty or information gain, and is therefore widely used to explain complex nonlinear behaviour in real-world systems. Attempting to analyse the analog world around us requires that we measure time in discrete steps, but doing so compromises our ability to measure entropy accurately. Various measures have been derived to estimate entropy (uncertainty) from discrete time series, each seeking to best capture the uncertainty of the system under examination. This has resulted in many entropy statistics from approximate entropy and sample entropy, to multiscale sample entropy and refined-composite multiscale cross-sample entropy.

As the number of statisitcal entropy measures grows, it becomes ever more difficult to identify, contrast and compare the performance of each measure. To overcome this, we have developed EntropyHub - an open-source toolkit designed to integrate the many established entropy methods into one package. The goal of EntropyHub is to provide a comprehensive set of functions with a simple and consistent syntax that allows the user to augment parameters at the command line, enabling a range from basic to advanced entropy methods to be implemented with ease.


It is important to clarify that the entropy functions herein described estimate entropy in the context of nonlinear dynamics, probability theory and information theory, and not thermodynamic or other entropies from classical physics.

Documentation & Help

The EntropyHub Guide is a .pdf booklet written to help you use the toolkit effectively (available for download here).
In this guide you will find descriptions of function syntax, examples of function use, and references to the source literature of each function.
The MatLab version of the toolkit has a comprehensive help section which can be accessed through the MatLab help browser under Supplementary Software.

Citation and Licensing

EntropyHub is licensed under the Apache License (Version 2.0) and is free to use by all on condition that the following reference be included on any scientific outputs realized using the software:

Matthew W. Flood
EntropyHub: An Open-Source Toolkit for Entropic Time Series Analysis,
PLoS One 16(11):e0259448 (2021),
DOI: 10.1371/journal.pone.0259448

© Copyright 2024 Matthew W. Flood, EntropyHub

Licensed under the Apache License, Version 2.0 (the “License”); you may not use this file except in compliance with the License. You may obtain a copy of the License at

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an “AS IS” BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

For Terms of Use see https://github.com/MattWillFlood/EntropyHub


If you find this package useful, please consider starring it on GitHub, Matlab File Exchange, PyPI , and Julia Packages as this helps us to gauge user satisfaction.

If you have any questions about the package, please do not hesitate to contact us at: info@entropyhub.xyz
If you identify any bugs, please contact us at: fix@entropyhub.xyz
If you need any help installing or using the toolkit, please contact us at: help@entropyhub.xyz

Thank you for using EntropyHub.