`Thermodynamics' of Minimal Surfaces and Entropic Origin of Gravity

TL;DR

This paper explores the thermodynamic properties of minimal surfaces in static spacetimes, proposing that gravity may originate from entropic principles linked to holographic screens and quantum entanglement.

Contribution

It derives a universal formula for area changes of minimal surfaces under particle shifts, supporting the entropic origin hypothesis of gravity.

Findings

Established a thermodynamic framework for minimal surfaces.

Linked gravitational entropy to quantum entanglement.

Supported the holographic interpretation of gravity.

Abstract

Deformations of minimal surfaces lying in constant time slices in static space-times are studied. An exact and universal formula for a change of the area of a minimal surface under shifts of nearby point-like particles is found. It allows one to introduce a local temperature on the surface and represent variations of its area in a thermodynamical form by assuming that the entropy in the Planck units equals the quarter of the area. These results provide a strong support to a recent hypothesis that gravity has an entropic origin, the minimal surfaces being a sort of holographic screens. The gravitational entropy also acquires a definite physical meaning related to quantum entanglement of fundamental degrees of freedom across the screen.