A New Entropic Force Scenario and Holographic Thermodynamics

TL;DR

This paper introduces a novel holographic gravity framework using a surface stress tensor and Brown-York energy, differing from Verlinde's approach, and explores its thermodynamic properties.

Contribution

It presents a new holographic gravity scenario with a surface stress tensor and analyzes its thermodynamics, contrasting it with Verlinde's entropic gravity proposal.

Findings

Surface stress tensor proportional to extrinsic curvature.

Holographic thermodynamics includes a chemical potential.

Verlinde's approach does not produce consistent thermodynamics.

Abstract

We propose a new holographic program of gravity in which we introduce a surface stress tensor. Our proposal differs from Verlinde's in several aspects. First, we use an open or a closed screen, a temperature is not necessary but a surface energy density and pressure are introduced. The surface stress tensor is proportional to the extrinsic curvature. The energy we use is Brown-York energy and the equipartiton theorem is violated by a non-vanishing surface pressure. We discuss holographic thermodynamics of a gas of weak gravity and find a chemical potential, and show that Verlinde's program does not lead to a reasonable thermodynamics. The holographic entropy is similar to the Bekenstein entropy bound.