How to proceed with nonextensive systems at equilibrium?

TL;DR

This paper discusses the limitations of additive energy in nonextensive systems at equilibrium and advocates for generalized statistics based on thermodynamic stationarity, clarifying the relationship between Tsallis and Rényi entropies.

Contribution

It introduces a framework for analyzing nonextensive systems using generalized statistics and clarifies the non-equivalence of Tsallis and Rényi entropies at equilibrium.

Findings

Additive energy is inadequate for nonextensive systems at meta-equilibrium.

Nonadditive energy or entropy systems require generalized statistical descriptions.

Tsallis and Rényi entropies are generally not equivalent.

Abstract

In this paper, we show that 1) additive energy is not appropriate for discussing the validity of Tsallis or R\'enyi statistics for nonextensive systems at meta-equilibrium; 2) $N$-body systems with nonadditive energy or entropy should be described by generalized statistics whose nature is prescribed by the existence of thermodynamic stationarity. 3) the equivalence of Tsallis and R\'enyi entropies is in general not true.