Group structure as a foundation for entropies

TL;DR

This paper explores the abstract concept of entropy as a functional on probability spaces, proposing a systematic classification based on properties like handling non-interacting systems and extensivity.

Contribution

It introduces a framework for classifying entropies using group structure, emphasizing the importance of extensivity and non-interacting systems.

Findings

Provides a classification scheme for entropy functionals

Highlights the role of group structure in understanding entropy

Connects entropy properties with physical and informational contexts

Abstract

Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and merits. Here we consider entropy in an abstract sense, as a functional on a probability space and we review how being able to handle the trivial case of non-interacting systems together with the subtle requirement of extensivity allows a systematic classification of the functional form.