# Tsallis entropy and generalized Shannon additivity

## TL;DR

This paper examines the axiomatic foundations of Tsallis entropy, focusing on the generalized Shannon additivity axiom, and characterizes Tsallis entropy for most parameter values.

## Contribution

It provides a simplified axiomatic characterization of Tsallis entropy based on Shannon additivity, excluding specific cases where $ ext{α}=1,2$.

## Key findings

- Shannon additivity characterizes Tsallis entropy for most parameters.
- The cases $ ext{α}=1,2$ require separate analysis.
- The axiomatic approach clarifies the foundational differences from Shannon entropy.

## Abstract

The Tsallis entropy given for a positive parameter $\alpha$ can be considered as a modification of the classical Shannon entropy. For the latter, corresponding to $\alpha=1$, there exist many axiomatic characterizations. One of them based on the well-known Khinchin-Shannon axioms has been simplified several times and adapted to Tsallis entropy, where the axiom of (generalized) Shannon additivity is playing a central role. The main aim of this paper is to discuss this axiom in the context of Tsallis entropy. We show that it is sufficient for characterizing Tsallis entropy with the exceptions of cases $\alpha=1,2$ discussed separately.