Tsallis entropy and hyperbolicity

TL;DR

This paper explores the hyperbolic properties of Tsallis entropy and its potential advantages over Boltzmann-Gibbs entropy in describing systems with long-range interactions.

Contribution

It introduces a metric formalism to analyze the composition properties of Tsallis entropy and investigates its hyperbolic nature and implications for such systems.

Findings

Tsallis entropy exhibits hyperbolic geometric properties.

Differences in composition rules between Tsallis and Boltzmann-Gibbs entropies are analyzed.

Preliminary evidence supports Tsallis entropy's effectiveness for long-range interacting systems.

Abstract

Some preliminary evidence suggests the conjecture that the collective behaviour of systems having long-range interactions may be described more effectively by the Tsallis rather than by the Boltzmann/Gibbs/Shannon entropy. To this end, we examine consequences of the biggest difference between these two entropies: their composition properties. We rely on a metric formalism that establishes the "hyperbolic" nature of Tsallis entropy and explore some of its consequences for the underlying systems. We present some recent and some forthcoming results of our work