# Tsallis and Kaniadakis statistics from the viewpoint of entropic gravity formalism

## TL;DR

This paper explores how Tsallis and Kaniadakis non-Gaussian statistics can be derived from entropic gravity formalism, affecting gravitational stability criteria and possibly explaining deviations in Newton's law at small scales.

## Contribution

It introduces a novel approach linking non-Gaussian statistics to entropic gravity, providing new insights into gravitational stability and potential deviations in gravity.

## Key findings

- Modified Jeans mass criterion with non-Gaussian statistics
- Altered free fall time in self-gravitating systems
- Potential connection to deviations of Newton's law at submillimeter scales

## Abstract

It has been shown in the literature that effective gravitational constants, which are derived from Verlinde's formalism, can be used to introduce the Tsallis and Kaniadakis statistics. This method provides a simple alternative to the usual procedure normally used in these non-Gaussian statistics. We have applied our formalism in the Jeans mass criterion of stability and in the free fall time collapsing of a self-gravitating system where new results are obtained. A possible connection between our formalism and deviations of Newton's law of gravitation in a submillimeter range is made.