Verlinde's emergent gravity in an $\boldsymbol{n-}$dimensional, non-additive Tsallis' scenario

TL;DR

This paper explores how non-additive Tsallis' q-statistics in n-dimensional phase space can model emergent gravity via entropic forces, capturing phenomena like confinement and asymptotic freedom.

Contribution

It integrates Tsallis' non-additive entropy with Verlinde's emergent gravity framework in higher dimensions, providing a novel statistical mechanics approach to gravitational phenomena.

Findings

Demonstrates entropic force can mimic confinement effects.

Shows the approach reproduces asymptotic freedom.

Provides a classical phase-space model in n dimensions.

Abstract

This paper brings together four distinct but very important physical notions: 1) Entropic force, 2) Entropy-along-a-curve, 3) Tsallis' q-statistics, and 4) Emergent gravitation. We investigate the non additive, classical (Tsallis') q-statistical mechanics of a phase-space curve in $n$ dimensions (3 dimensions, in particular). We focus attention on an entropic force mechanism that yields a simple realization of it, being able to mimic interesting effects such as confinement, hard core, and asymptotic freedom, typical of high energy physics