Which entropy for general physical theories?

TL;DR

This paper investigates which entropy functions best quantify information content in general physical theories, demonstrating that no single entropy universally serves this purpose across different theoretical frameworks.

Contribution

It introduces a systematic evaluation of multiple entropy functions within a toy theory, showing the limitations of existing entropic measures for general theories.

Findings

No single entropy universally quantifies information content in all theories.

Different entropy functions behave variably in the Bilocal Classical Theory.

Classical and quantum entropies are specific cases within a broader context.

Abstract

We address the problem of quantifying the information content of a source for an arbitrary information theory, where the information content is defined in terms of the asymptotic achievable compression rate. The functions that solve this problem in classical and quantum theory are Shannon's and von Neumann's entropy, respectively. However, in a general information theory there are three different functions that extend the notion of entropy, and this opens the question as to whether any of them can universally play the role of the quantifier for the information content. Here we answer the question in the negative, by evaluating the information content as well as the various entropic functions in a toy theory called Bilocal Classical Theory.