Tsallis' thermostatitics, MOND theory and holographic considerations on a Machian Universe

TL;DR

This paper integrates Tsallis' non-extensive thermodynamics, Verlinde's entropic gravity, and MOND theory within a Machian universe framework, deriving new cosmological parameters and exploring holographic entanglement.

Contribution

It establishes a novel connection between Tsallis statistics, entropic gravity, and MOND, deriving cosmological parameters and proposing holographic entanglement in this context.

Findings

Calculated Hubble parameter and universe age using Tsallis formalism.

Derived a new value for the Tsallis parameter based on Mach's principle.

Proposed new forms for MOND ingredients from entropic gravity.

Abstract

MOND theory explains the rotation curves of the galaxies. Verlinde's ideas establishes an entropic origin for gravitational forces and Tsallis principle generalizes the theory of Boltzman-Gibbs. In this work we have promoted a connection between these recent approaches, that at first sight seemed to have few or no points in common, using the Mach's principle as the background. In this way we have used Tsallis formalism to calculate the main parameters of the Machian Universe including the Hubble parameter and the age of the Universe. After that, we have also obtained a new value for the Tsallis parameter via Mach's principle. Using Verlinde's entropic gravity we have obtained new forms for MOND's well established ingredients. Finally, based on the relations between particles and bits obtained here, we have discussed the idea of bits entanglement in the holographic screen.