# Quantum statistical treatment of Verlinde's conjecture in a Tsallis framework

## TL;DR

This paper explores Verlinde's conjecture within a quantum statistical framework using Tsallis' entropy, demonstrating that it acts as an effective potential energy and recovers Newtonian gravity in the classical limit.

## Contribution

It extends Verlinde's entropic gravity hypothesis to quantum systems with Tsallis' entropy, showing its role as potential energy and classical Newtonian behavior.

## Key findings

- Tsallis' entropy functions as potential energy in quantum systems.
- Emergent force exhibits Newtonian dependence in the classical limit.
- The framework generalizes classical entropic gravity to quantum and non-extensive contexts.

## Abstract

Verlinde has recently conjectured, via a Beckenstein-like thought experiment, that gravitation, instead of being an elementary force, is an emergent entropic one. This rather surprising conjecture was actually proved in [Physica A {\bf 505} (2018) 190], in a strictly classical statistical mechanics' environment. In this Communication, we work in a quantum statistical context to consider the conjecture in the case of bosons/fermions, in a Tsallis' framework. We prove that Tsallis' entropy is the operating potential energy in this quantum treatment, something that does not happen in the case of Boltzmann-Gibbs' entropy. \color{red} In the classical limit, we show that the emergent force has a Newtonian dependence with the distance.