Notes on microstates, Tsallis statistics and entropic gravity formalism

TL;DR

This paper explores the connection between gravity, thermodynamics, and holographic principles, analyzing entropy and modified dynamics in various scenarios, including cosmology, to understand gravity as an emergent phenomenon.

Contribution

It introduces a nonrelativistic analysis of holographic screens and derives modified Newtonian dynamics from entropic gravity concepts.

Findings

Disclosed MOND from Verlinde's ideas

Calculated cosmological elements using entropic approaches

Analyzed entropy behavior on holographic screens in different scenarios

Abstract

It is an old idea to realize Einstein's equations as a thermodynamical equation of state. Since then, there has been new conjectures to understand gravity from another point of view. In this way we can accept that the gravitational field is not an underlying one like an emergent force from other approaches based on the knowledge of relativity, quantum and black holes thermodynamics, and different statistical formalisms. One important question concerning this gravity/thermostatistics correspondence is whether the holographic screen could be well defined for a nonrelativistic case of a source mass. Hence, to understand the actual role of the holographic screen is a very relevant issue. In this letter we have analyzed the entropy as a function of the holographic screen in some different scenarios. We have disclosed modified Newtonian dynamics (MOND) from Verlinde's ideas. Besides, we have calculated some cosmological elements using the same ideas. The results obtained using MOND will guide us to obtain other cosmological results.