# A two-parameter entropy and its fundamental properties

## TL;DR

This paper introduces a new two-parameter generalized entropy that encompasses Tsallis and Shannon entropies, exploring its fundamental properties and comparing its information-theoretic and geometric characteristics.

## Contribution

It proposes a novel two-parameter entropy and analyzes its key properties, extending the understanding of generalized entropies beyond existing models.

## Key findings

- The new entropy reduces to Tsallis and Shannon entropies at specific parameters.
- It satisfies sub-additivity, strong sub-additivity, joint convexity, and information monotonicity.
- The entropy exhibits distinct information-geometric properties compared to classical entropies.

## Abstract

This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and the Shannon entropy for specific values of its parameters. We develop a number of information-theoretic properties of this generalized entropy and divergence, for instance, the sub-additive property, strong sub-additive property, joint convexity, and information monotonicity. This article presents an exposit investigation on the information-theoretic and information-geometric characteristics of the new generalized entropy and compare them with the properties of the Tsallis and the Shannon entropy.