Heat capacity of Holographic screen inspires MOND theory

TL;DR

This paper proposes a novel connection between holographic screen thermodynamics and MOND gravity, deriving the MOND interpolating function from heat capacity considerations of a q-deformed fermionic system.

Contribution

It introduces a model where the heat capacity of holographic screen degrees of freedom leads to MOND-like behavior, linking emergent gravity with quantum statistical mechanics.

Findings

Heat capacity per degree of freedom inspires the MOND interpolating function.

MOND acceleration is derived as a function of Planck acceleration.

Both ultra-relativistic and non-relativistic statistics are analyzed.

Abstract

It is argued that Planck mass may be considered as a candidate for the mass content of degrees of freedom of holographic screen. In addition, employing the Verlinde hypothesis on emergent gravity and considering holographic screen degrees of freedom as a $q$-deformed fermionic system, it is obtained that the heat capacity per degree of freedom inspires the MOND interpolating function. Moreover, the MOND acceleration is achieved as a function of Planck acceleration. Both ultra-relativistic and non-relativistic statistics are studied.