Realize Emergent Gravity to Generic Situations

Abstract: We clarify the problem in which occasions can gravitational force be regarded emergent from thermodynamics, by proposing an entropic mechanism that can extract the entropic gradient existing in spacetime, due to the variation of the Casini-Bekenstein bound in specific quasi-static processes with the heat flux $\delta Q$ into the whole casual wedge. We explicitly formulate the derivation of inertial force as the emergent gravitational attraction from the Entanglement First Law. We find the saturation of the bound along with the vanishing relative entropy corresponds to the variation of minimal surface. To covariant meaning, it is the Bousso bound. Besides, this understanding is connected to recent Pennington's work on Black Hole Information Paradox, suggesting a Page-Curve function origins from removing attraction by the external heat bath. Our theory from entanglement now overcomes several criticism towards Verlinde's original entropic force proposal, and is able to co-exist with Susskind's Complexity Tendency. This entropic mechanism reproduces the Newton's Second Law in Rindler space and the gravitational force (together with derivation of the Einstein equation) beyond the near-horizon region, and can be adapted into AdS/CFT and other generic situations.