Look beyond additivity and extensivity of entropy for black hole and cosmological horizons

TL;DR

This paper compares various nonextensive and nonadditive entropy formulations beyond Boltzmann-Gibbs, analyzing their properties and relevance to black hole and cosmological horizons with long-range gravitational interactions.

Contribution

It systematically examines the properties and relations of nonextensive entropies and their applicability to gravitational systems, providing comprehensive tables for the community.

Findings

Nonextensive entropies often break additivity in gravitational systems.

Relations between different nonextensive entropies are clarified.

Implications for horizon thermodynamics in black holes and cosmology.

Abstract

We present a comparative analysis of the plethora of nonextensive and/or nonadditive entropies which go beyond the standard Boltzmann-Gibbs formulation. After defining the basic notions of additivity, extensivity, and composability, we discuss the properties of these entropies and their mutual relations, if they exist. The results are presented in two informative tables supposedly of strong interest to gravity and cosmology community in the context of intensively explored recent days the horizon entropies for black hole and cosmological models. This is since gravitational systems admit long-range interactions which usually lead to a break of the standard additivity rule for thermodynamical systems composed of subsystems in Boltzmann-Gibbs thermodynamics. The features of additivity, extensivity, and the composability are listed systematically. Some brief discussion on the validity of the notion of equilibrium temperature for nonextensive systems is also presented.