📝 SummarXiv

Abstract

The Gibbons-Hawking-York (GHY) approach was developed for a Euclidean path integral derivation of equilibrial black hole entropy. To extend it to a near-equilibrium Euclidean path integral, we study a static Euclidean shell model. We calculate the Euclidean action shift for the static simple model thin shell held just outside the horizon, and find agreement with Casini's version of Bekenstein bound. We find a negative entropy deficit associated to the gravitational attraction towards the shell. For a holographic interpretation, the deficit corresponds precisely to the apparent horizon area deviation from the extremal surfaces Therefore, we develop a Euclidean path integral framework in which gravitational force emerges from negative entropy gradients due to Hawking temperature gradients. This setup allows us to introduce Onsager reciprocity and a linear-response relation to build a dissipating system, and treat the configuration as a near-equilibrium steady state (NESS). This clarify that the gravitational potential is a phenomenon informational and ordering, rather than entropic and disordering.