First law of thermodynamics on holographic screens in entropic force frame

TL;DR

This paper derives the first law of thermodynamics on holographic screens surrounding black holes within the entropic force framework, linking thermodynamics, gravity, and holography.

Contribution

It formulates the differential and integral first law on holographic screens, connecting thermodynamics with black hole geometry in the entropic force paradigm.

Findings

First law consistent with equipartition principle

Holographic screen entropy relates to area as S=A/4

Metric expressed via thermodynamic variables

Abstract

By following the spirit of Verlinde's entropic force proposal arXiv:1001.0785, we give the differential and integral form of the first law of thermodynamics on the holographic screen enclosing a spherical symmetric black hole. It is consistent with equipartition principle and the form of Komar mass. The entropy of the holographic screen determines its area, i. e. $S=\frac{A}{4}$. And then we express the metric by thermodynamic variables, to give an illustration of how the space is foliated by the thermodynamical potentials.