ENTROPIC FORCE AND ITS FLUCTUATION IN EUCLIDEAN QUANTUM GRAVITY

In this paper, we study the idea about gravity as entropic force proposed by Verlinde. By interpreting Euclidean gravity in the language of thermodynamic quantities on holographic screen, we find the gravitational force can be calculated from the change of entropy on the screen. We show that normal gravity calculation can be reinterpreted in the language of thermodynamic variables. We also study the fluctuation of the force and find the fluctuation acting on the point-like particle can never be larger than the expectation value of the force. For a black hole in AdS space, by gauge/gravity duality, the fluctuation may be interpreted as arising from thermal fluctuation in the boundary description. And for a black hole in flat space, the ratio between fluctuation and force goes to a constant T/m at infinity.