Power-law entropies for continuous systems and generalized operations

TL;DR

This paper discusses the definition and interpretation of power-law entropies for continuous systems, emphasizing the importance of generalized algebraic operations induced by these entropies, with a focus on Tsallis entropy.

Contribution

It introduces a perspective that considers generalized addition and multiplication operations for power-law entropies, clarifying their meaning in continuous systems.

Findings

Generalized operations are crucial for understanding power-law entropies.

The approach is exemplified using Tsallis entropy.

Provides a new framework for continuous system entropies.

Abstract

We present our view in a standing debate about the definition and meaning of power-law entropies for continuous systems. Our suggestion is that such arguments should take into account the generalized operations of addition and multiplication induced by the power-law entropies' composition properties. To be concrete, we highlight our view using the case of the $q$- also known as "Tsallis", entropic functionals.