Entropic force and its fluctuation in Euclidian quantum gravity

TL;DR

This paper investigates gravity as an entropic force using gauge/gravity duality, deriving force and its fluctuations without relying on equipartition, and provides insights into the duality and fluctuation limits.

Contribution

It introduces a method to derive entropic gravity from dual field theories without equipartition assumptions, enhancing understanding of gauge/gravity duality and force fluctuations.

Findings

Force fluctuation never exceeds the expected force value.

In AdS black holes, fluctuations are due to thermal effects from the boundary field theory.

For flat space black holes, fluctuation-to-force ratio approaches T/m at infinity.

Abstract

In this paper, we study the idea about gravity as entropic force proposed by Verlinde. By applying the identification between partition functions of gravity theory and the dual field theory, we find the gravitational force can be calculated from the changing of entropy induced from its dual field theory side. Unlike Verlinde's calculation, our method does not depend on other assumptions such as equipartition of energy, so it is a safe check on the entropic force idea. Also we show how entropic force can be derived by similar method from gravity side along, which will provide a clue to a better understanding on the gauge/gravity duality. At last, we study the fluctuation of the force, and we find the fluctuation acting on the point-like particle can never be larger than the expectation value of the force. For black hole in AdS space, by gauge/gravity duality, the fluctuation is induced by thermal fluctuation from field theory living on conformal boundary. And for the metric of black hole in flat space, the ratio between fluctuation and force goes to a constant$\frac{T}{m}$ at infinity. .